I'm not a wind player but I do have long term experience (40 years) with dentures.
In my personal experience a full set "work" better than a partial set. I have a full set with a metal plate (which is a stainless steel casting) and they are as rock-solid as normal teeth. In fact at the first fitting of the plate, it "stuck" in place so firmly it took the dentist about 10 minutes to remove it! I wear them 24/7/365 and basically never think about them. The plate has also lasted "for ever" - it's now more than 30 years old and works as well as when new.
They are held in place by the surface tension in the saliva which fills the (tiny) gap between the plate and the mouth structure - not by being a mechanical "tight fit". The thinner the saliva layer (i.e. the more accurate the fit) the firmer the grip.
From my personal experience I think a mixture of natural teeth and individual implants may be more problematic, since natural teeth move around in the gums as a person ages, but implants do not. Certainly, partial denture plates don't work so well, since as the natural teeth grow and move the shape of the gums changes and the fit with the denture plate becomes worse.
Note also, in the UK you can get a "full set of implants" which is effectively a denture attached to only 3 or 4 fixing points in the jaw, not a separate implant for each tooth. That should reduce the costs compared with "individual tooth implants" - but I don't know anything about the US healthcare cost structure (except that, viewed from the rest of the world, it seems extortionate).
Some of these options may involve removing healthy teeth - which is an irreversible procedure, of course. Professional advice, both musical and dental, would seem a very wise course to take.