I can't say "..." it would ruin the dialogue and also I'm supposed to support the users perspective.
Some personal counsellors ask questions, along the lines of, "And how do you feel about that?"
Maybe that's similar to Vipasanna's asking people to note their feelings.
Maybe that turns people's attention inward (not "my partner is wrong" but "I'm feeling ignored" or "confused and angry about my inability to make my partner behave the way I want them to") which might be essential to helping them to act, "rationally" or sanely.
Maybe asking 'leading' questions is an acceptable way to steer the conversation. By analogy with a medical doctor they could be 'informed' questions (i.e. informed by your prior knowledge), but still I suppose they ought to be questions (I read a science fiction story once in which a society had a jury system where the jury members were expected to be "biased" but not allowed to be "prejudiced").
Beware that I'm not "a so-called professional", but your professional page (which you linked to) says,
In addition to providing the caller with information about alcohol and drugs, and suggesting appropriate services for treatment of substance abuse, the counsellors practice the «professional conversation». The counsellors’ role is not to judge or moralize, but, by listening and asking the right questions, unveiling the solutions which best suits the caller’s situation.
I have a very firm conviction about what would be a good way for them to suffer less, how can I best convey this?
The quote above says there are "appropriate services for treatment".
Do you agree whether those services exist? And whether they're appropriate? Is it your job to be/supply those services, or is it your job to suggest those services?
Does your meditation on the three marks suggest ways in which those services could be improved or augmented? Is there someone (e.g. your boss and/or counsellor) with whom you can discuss whether to add to the services or solutions which are "suggested as appropriate" by the agency which employs you?
Also if you want to or are able to "use personal experience" in a way that not appropriate for your job, there are vehicles for doing that outside the scope of your employment -- I'm thinking that AA / Al-Anon or NA / Nar-Anon meetings, for example, centre around people recounting their personal experience and insight for the benefit of others.
I sometimes think that "if only the users of our service could think like that, it would be so much easier for them".
That reminds me of (among other things) this scene in a movie, As Good as It Gets, where the girl is wooed by an antihero and cries out, "Why can't I just have a normal boy-friend? Why? Just a regular boy-friend who doesn't go nuts on me?" At that point her mum, who's listening behind the door, pops out and says, "Everybody wants that, dear. It doesn't exist. Oh I'm sorry. I didn't mean to interrupt."
If you want to meet people who've already solved their personal problems then I guess you need a different job (or to meet other people outside the scope of your job).
If you're saying "If only other people had the same views as I have then they wouldn't have a problem", I think you're not the first person to have said that. :-)
how can I best convey this?
Maybe be clearer about what you're trying to convey. Compassion? Your description of a universal solution? An environment in which someone sees their own way out of their problem? An emotional intensity, neither too little (complacency) nor too much (despair)? Professional (legal or psychiatric) help? An independent (e.g. not "co-dependent") perspective on what's right and wrong? A life-line? ...?