The problem I encounter is not with my knees but my lower back.
This can be remedied for most people.
My problem relates primarily to the "tailbone" (whatever it's really called) being too horizontal (compared to most people). Chiropractors have been able to make a bit of improvement on it, though what you say about having lowered knees relative to the hips might well help alleviate the resultant pressure... I'll give it a go.
a long time ago, when I was first being trained in basic meditation, a monk told me to roll a towel up tightly so that it forms a kind of rod, and push that just
under the tailbone (when already seated on a cushion, of course). This has the effect of just raising it a little, and this eases some of the strain on the lower back. I have modified it slightly, though. I first start with some newspaper and roll that
into a thin rod; then I wrap the towel around that,
and I end up with a rod that is a good balance between firmness and softness.(You need to keep the pressure up, on both newspaper and towel as you roll them together, or the result is too 'mooshy'. Also, don't use too large a towel, for the same reason.) I've used this method for years, and it keeps my lower back from getting sore, even though I sit in half-lotus on a cushion, on the floor. I recommend it highly. (By the way, because towels are kind of rough in texture, the rod lasts and does not fall apart, just keep it nicely rolled up, and use in the next session too. I only have to 're-roll' them about once every two weeks.)