Wow--Lots of terrific pointers here that I'll have to try, and a couple of comments...
1) I have a "tempo" for *every* new piece I learn, regardless of instrument: it's "geriatico" (i.e. andante with a walker and oxygen bottle)
2) there's something to be said for *NOT* playing a piece for awhile. I've been struggling with Miss McLeod's Reel for about 20 years (no foolin'). I work at it for six months or so and give up in frustration. (I still practice other material though) When I come back to it a month later, I usually find that whatever was hanging me up has somehow fixed itself, and I've got a different problem to rassle with.
$0.02, fwiw. I've been playing (you name it) on and off for over 30 years, and I'm still striving for speed, precision, and feeling on every(any?) instrument. Haven't succeeded yet, but still trying!