In my opinion, meditation on death is good for reducing the naive infatuation with sensual pleasures and the overall heedlessness coming from "intoxication with youth" and "intoxication with health". However, it does not address the more subtle root of suffering, what OP called "attachment to the body's continued existence".
According to Mahayana explanations, although attachment to body as "me, mine" seems obvious and well-based, it is in fact pretty arbitrary. In traditional Lam-Rim literature there are descriptions of hellish states caused by confused identification with other arbitrary objects. Imagine the pain someone experiences when they think they are a door, craving the peace but constantly getting slammed instead.
From Mahayana perspective, our confused identification with a living organism comes from our egotism. We have this deep habit of chasing our personal goals and contrasting them with the goals of other beings. (This works similar to the Stockholm Syndrome, when the hostage temporary aligning with the captor's goals leads to the hostage identifying (bonding) with the captor. In this case the captor is our body or more broadly our social persona). Instead, the Mahayana solution to the identification problem is deconstructing one's ego, first and foremost through the practice of altruism. Indeed, taking an active interest in other people's well-being assists in switching one's focus from "self" to "all" - which reduces and eventually eliminates attachment to an individual organism.
The Mahayana Buddhist term for this is "bodhi-citta", the mind of the Buddha. A simple explanation of bodhicitta is when we make the entire world our business, no longer restricting our sense of care to just ourselves and our close circle.
Coming back to the self-identification, the Buddha explained it like this (in my interpretation):
- Aging, decay, death come from the fact that we are born
- Birth comes from the fact that we identify with a living being
- Individualized existence comes from the egocentric activity
- Egocentric activity comes from craving
- Craving comes from the memory of a good feeling
- The memory of a good feeling comes from experience of a contact
- Experience of a contact comes from the experience of the boundary between the external and the internal
- Experience of the boundary between the external and the internal comes from the objectification
- Objectification comes from the mind constructing/interpreting the world
- The mind constructing/interpreting the world comes from the accumulation of random imprints and memories
- Accumulation of random imprints and memories comes from not knowing how things work.
The multiple ways to break this chain are either: to stop the egocentric activity, or to give up craving, or to stop objectification (via analytical deconstruction of the mind-made models to see their emptiness), or to stop constructing/interpreting the world (by non-maintaining the narratives, non-abiding), or to gain a direct insight into how things work.
- the Buddha gained insight into how things work,
- therefore the Buddha no longer accumulates random imprints and memories,
- the Buddha no longer naively constructs/interprets the world,
- the Buddha no longer naively objectifies the experience,
- the Buddha no longer naively assume the boundary between the outer and the inner,
- the Buddha no longer naively experiences the contact,
- the Buddha no longer naively enjoys the good experience,
- the Buddha no longer craves the object of good experience,
- the Buddha no longer acts egoistically towards the object of craving,
- the Buddha no longer identifies oneself as the same one who craves, the same one who acts, and the same one who enjoys the result,
- the Buddha no longer has a notion of "I have been born as this human being",
- the Buddha no longer has a notion of "I age, decay and will eventually die"
Something like this. This may be a little rough around the edges - please don't get hung up on the details -- but it should give you an idea of the overall approach.