Back in my flute-playing days I learned an interesting metronome technique that involved off-setting the clicks of the metronome so that the clicks would sound on the off beats. I start my off-beat "machine" kind of like the way you start a game of jumprope (when someone else is doing the turning). In simple meter (divisions of two or four) I set it up so that the clicks happen on 2 and 4, and then feel the emphasis on the silent 1 and the silent 3. It sets up a nice even groove (as it should).
I often use this method to "notch" a passage from a slow tempo to a faster tempo. On the slow end of the tempo spectrum it feels kind of like ironing. You can almost watch groups of sixteenth notes become more even. As you "notch" up the tempo it's easy to see and hear the exact configurations of pitches that need attention. On the slower end of the notching experience it is easy to concentrate on how the bow or the tongue need to behave to insure that the notes are even. The places that rush become immediately apparent as you notch up the off-beats.
It is difficult, at first, to play more than a line or two of constant sixteenth notes without creeping into "downbeat" mode, but with practice, observations, patience, and forgiveness, practicing this way is really rewarding.
Last night I decided to practice a slower lyrical passage that was giving me trouble using off beats. The passage in question actually has off beats in the piano part. My challenge was (and still is) to play the on-the-beat notes with enough oomph and gusto (not to mention vibrato) to allow the music to ebb and flow the way I wanted it to. I found myself having trouble beginning held notes with vibrato because I had gotten so used to depending on the on-beat impulse to propel the vibrato. I also noticed, at the slower tempo, that concentrating on off beats and playing sustained double stops are difficult things to do simultaneously.
So I "notched" the passage down, doing just the opposite of what I would do if I were practicing a passage that I wanted to play fluently at a faster tempo. Doing this proved to be a sort of clean window into the body of the sustained notes, and after about half an hour of frustration I was able to have better control over the whole span of any given note in the passage, not just its beginning and its end.
We so often forget that the duration of a note is where the music happens. And our awareness of that fact is something that we face anew every day.