this might be a dumb idea, but could you just take out the gravel gradually, and replace it with new? Like maybe find some sort of divider you could use and just do a small section at a time? Or just push alot of it to one side and make it deeper for a little while as you make the transition? I would think even if its not perfect you could hide the few bits of old gravel you miss, then the new stuff could be gradually building up bacteria
Alot of gravel vacs before you start to move things should help keep the waste stirred up to a minimum. I realize its only one fish, but I've kept up with my 10 gallon betta tank very well, and I hardly ever see anything vacummed out when I do it!!