This is exactly what I do, except I use recordings, and the slowdowner, instead of MIDIs. I try my best to give my MIDIs the proper rolls and stuff, but they’re still a far cry from listening to the real thing.
When I was a beginner, things took longer, but these days, this is pretty much how I learn a tune:
Find the sheet music, listen to a few recordings, finding those with variations I like.
Mark up my sheet music, learn the bits.
Try to put away the sheet music within 10 reps, playing solely from memory.
Practice the tune about a week, solo
Bring the tune to session, and try to fit in, on my quietest whistle. Invariably, I’ll need to refine the tune.
If needed, use the speed-up technique described above. It really helps train the trickier passages if I’m having trouble nailing it at speed.
Work on my own style, continue to practice the tune outside of session. This is true even for tunes I’ve been playing years, of course!
I find that the more I play in sessions, and the more I play in general, the less I have to do the slow-downer thing. I imagine this is true for everyone, so it’s just a matter of keeping at it, and continuing to actively listen.
One thing I might suggest is to pick one of the tune types (jigs, reels, polkas, hornpipes) and learn a bunch of them by heart. What you’ll find is that within the tune types there are a lot of similar phrases. For example, jigs have lots of “AGG” type, the “BAB” type and so on. As you become familiar with these patterns you’ll play them as patterns (rather than 3 separate notes) and that will naturally speed you up.
Another good practice technique (stolen from Suzuki) is to immediately repeat a phrase when you make a mistake. If you make a mistake again, play the phrase ten times correctly. This is advice I could stand to follow more closely myself. Learning the tune correctly and getting “finger memory” is half the battle for getting up to speed. And the only way to get finger memory is through repetition.
As a beginner, I was trying to get up to speed on a tune (“Blackthorn Stick”) and posted a link to the recording of it here, asking if this was unusually fast. I got back a few puzzled replies that said “Seems nice and leisurely.” It was very depressing.
Now, a couple of years later I can play that tune and many others at “session speed”. But the speed came very slowly and only with lots of practice. It’s tough to be a “dabbler” in traditional music because you simply can’t develop and maintain the skills you need. On the positive side, you’ll find playing Christmas carols, folk songs and so on quite leisurely by comparison