There's a Dhamma talk titled "Selves & Not-self". The second part of it, Talk 2: Out of the Thicket and Onto the Path discusses the sutta that you're asking about.
That article is too long to quote but it's short enough to read.
The use of "the Thicket" in the title is presumably a reference to this passage in MN 2,
As he attends inappropriately in this way, one of six kinds of view arises in him: The view I have a self arises in him as true & established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self... or the view It is precisely by means of not-self that I perceive self arises in him as true & established, or else he has a view like this: This very self of mine — the knower that is sensitive here & there to the ripening of good & bad actions — is the self of mine that is constant, everlasting, eternal, not subject to change, and will stay just as it is for eternity. This is called a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, & death, from sorrow, lamentation, pain, distress, & despair. He is not freed, I tell you, from suffering & stress.
I think this passage (from MN 2 above) helps to explain why the Buddha wouldn't want to declare whether or not "there is a self".
I think it's saying that "I have a self" is a view, and "I have no self" is another view.
They are "fetters of views" (or become fetters) ... as opposed to "right view":
The well-instructed disciple of the noble ones... discerns what ideas are fit for attention, and what ideas are unfit for attention. This being so, he does not attend to ideas unfit for attention, and attends [instead] to ideas fit for attention... He attends appropriately, This is stress... This is the origination of stress... This is the cessation of stress... This is the way leading to the cessation of stress. As he attends appropriately in this way, three fetters are abandoned in him: identity-view, doubt, and grasping at precepts & practices.
Further to that I think there's another sutta, I don't remember which sutta but the following is a quote from an article This is not me; this is not mine, I am not this by Bodhipaksa,
The Buddha did not teach, incidentally, that there was no self. The word “anatta,” which is often translated as “no self” is invariably used in the Buddhist scriptures in the context of saying “This is not myself. That is not myself.” It’s never used, as far as I’m aware, to say “there is no self.” And in fact when the Buddha was asked flat out if he taught that there was no self he refused to answer, and he also said that there was no view of self that would not lead to suffering: including the view that there is no self. I do sometimes say there is “no self” but what I mean by that is that there is no self that exists as we think it exists: separate and permanent. That kind of self doesn’t exist.
Edited to add: Bodhipaksa was paraphrasing paragraph 23 of the The Discourse on the Snake Simile -- Alagaddupama Sutta (MN 22):
- "You may well accept, monks, the assumption of a self-theory from the acceptance of which there would not arise sorrow and lamentation, pain, grief, and despair. (But) do you see, monks, any such assumption of a self-theory?" — "No, Lord." — "Well, monks, I, too, do not see any such assumption of a self-theory from the acceptance of which there would not arise sorrow and lamentation, pain, grief and despair."
Re. the question in the OP, whether "the skandhas can be identified as a self", the footnote  says,
Attavaadupaadaanam upadiyetha. While in most translations the term upaadaana has been rendered by "clinging," we have followed here a suggestion of the late Bhikkhu Ña.namoli, rendering it by "assumption" [see The Wheel No. 17: Three Cardinal Discourses of the Buddha, p. 19 (Buddhist Publication Society, Kandy)]. In this context, the word "assumption" should be understood: (1) in the sense of a supposition, (2) in the literal sense of its Latin source: adsumere, "to take up," which closely parallels the derivation of our Paali term: upa-aadaana, "taking up strongly." In this sense we have used it when translating the derivative verb upaadiyetha by "you may accept." Attavaadupaadaana is one of the four types of clinging (see Nyanatiloka's Buddhist Dictionary), conditioned by craving (ta.nhaa). This term comprises, according to Comy, the twenty types of personality-belief (sakkaaya-di.t.thi).
Quoting this passage of our text, the Ven. Dr. Walpola Rahula remarks: "If there had been any soul-theory which the Buddha had accepted, he would certainly have explained it here, because he asked the monks to accept that soul-theory which did not produce suffering. But in the Buddha's view, there is no such soul-theory..." (What the Buddha Taught, London, 1959; p.58).
The so-called "twenty types of personality-belief" are listed in MN 44 as well as in SN 22.1 i.e. four types of belief for each of the 5 khandhas:
- That the khandha is the self
- That the self possesses the khandha
- That the khandha is in the self
- That the self is in the khandha
Dharmafarer has a similar translation of MN 22:
Bhikshus, you may well cling to the self-doctrine194 that would not cause sorrow, lamentation,
pain, grief and despair to arise in one who clings to it.195 But do you see any such possession, bhikshus?”
“Good, bhikshus. I, too, do not see any doctrine of self that would not arouse sorrow, lamentation, pain, grief and despair in one who clings to it.
Or perhaps you're asking whether it's OK to "consider" a khandha as self, as long as they're not taken to be unchanged?
Paragraph 23 of MN 22 says that you can't "cling to" (or "assume") a self-view that doesn't cause suffering.
Maybe your question hinges on whether you can "consider" (as it says in the question) or "believe" (as it says in the title) something (a belief or identification) that's impermanent? If so perhaps the answer is that words like "view" and "doctrine" and "belief" are taken to be somewhat fixed, not transient -- see for example the answers to this question, How are 'conceit' and 'identity-view' not the same?
I guess I need to leave it to you to decide whether your saying "skandhas can be as a self, as long as they aren't then taken to be in any way unchanged from moment to moment" matches something like SN 22.1,
Ven. Sariputta said: "Now, how is one afflicted in body & afflicted in mind?
There is the case where an uninstructed, run-of-the-mill person — who has no regard for noble ones, is not well-versed or disciplined in their Dhamma; who has no regard for men of integrity, is not well-versed or disciplined in their Dhamma — assumes form (the body) to be the self, or the self as possessing form, or form as in the self, or the self as in form. He is seized with the idea that 'I am form' or 'Form is mine.' As he is seized with these ideas, his form changes & alters, and he falls into sorrow, lamentation, pain, distress, & despair over its change & alteration.
(as well as 'form', likewise for feeling, perception, fabrications, and consciousness)
And how is one afflicted in body but unafflicted in mind? There is the case where a well-instructed disciple of the noble ones — who has regard for noble ones, is well-versed & disciplined in their Dhamma; who has regard for men of integrity, is well-versed & disciplined in their Dhamma — does not assume form to be the self, or the self as possessing form, or form as in the self, or the self as in form. He is not seized with the idea that 'I am form' or 'Form is mine.' As he is not seized with these ideas, his form changes & alters, but he does not fall into sorrow, lamentation, pain, distress, or despair over its change & alteration.
"That too has not been declared by the Blessed One: 'The Tathagata neither exists nor does not exist after death.'"See also Tetralemma.