
I am trying to play it myself too, struggling, but it is a lot of fun, notes are simple, but its bloody difficult to hit the right ones. Anyway, most Monk solos are beautifully and well-structured little masterpieces. I think that even he himself didnt think it very necessary for other people to improvise on it any further.
Good call on Monk's solos. Most people probably wouldn't think so, but he's like the poster child for sticking to the melody.
Probably because his tunes themselves are practically solos in themselves.
ETA Yeah, I remember a teacher a long time ago was all about Monk's ballad "Ask Me Now," and it was like, "Hell, you don't need to do some flash double-time solo....tune speaks for itself." Lots of those Monk tunes, like "Crepuscule." Or "Trinkle Tinkle" (I think that's the right spelling) — even when he's doing stride LH four to the bar on those Black Lion live recordings, he's never off the tune. He never even substitutes harmonies, AFAICR. "Ruby My Dear," right? Always just the melody, plus maybe a few little walking bits in tenths (and not just the tenths that are part of the head).
The opposite end would be doing some dogshit corny standards like "Paper Moon" or whatever, but, Monk kind of made his own gravy.
EETA, No, "Paper Moon," I've been playing in my car a few Kenny Drew albums and he does some crap tunes (IMHO) like that one and "Taking A Chance on Love," but, you know, Monk did a lot of those kinds of tunes too. I don't know what I was on about, but I'll tell you one thing: the only way I'd play something like "Just A Gigolo" is just like Monk did it. It's a real lesson to be able to get something going on those kinds of tunes. One of many lessons from Monk is how he can arrange the heads to those tunes, with some nice substitutions, and by the time he's done with his performance, solos and all, you never want to go back to straight block chords to play those kinds of tunes.

Point is (Monks) that Thelonious played it a lot better.
Word. That's probably one of the best examples of how to do it Monk style.
That could be a concert piece in itself, and not too hard to transcribe.
Of course it wouldn't quite be Monk without his unique style of using the crushes in RH, but I think a good piano player could cover it note for note. I'm not sure if that would be a good idea, but it would be certainly be a good practice.
ETA Oh, and I'm not trying to be like Mr Jazz here or anything: there's people here who went to UNT and studied with people like Dan Haerle. So, I'm really not trying to steal anybody's thunder, I just kind of hack away at this stuff and not trying to be some kind of authority. It's always just my opinion.
EETA Oh, I just heard the Joanna MacGregor version of the Monk tune. I don't want to criticize her, and I'm 100% sure she's a better pianist than me, but maybe that's not quite the way for that tune. It's a gutsy choice on her part, so lots of respect for even giving it a go. It's an interesting point of reference for how to approach Monk in a recital/concert setting, and I'm glad to have heard it. You know who does a lot of Monk tunes in concert with a fresh take? Fred Hersch. Yeah, he does it in a jazz context, but I'd check his stuff out for, especially for some of the deep cuts from some of Monk's earlier solo albums.
No, I can't criticize Ms. MacGregor at all — in fact, I think it's a great effort and maybe it brings more people to Monk's compositions and arrangement on that tune. In fact, I'll look forward to hearing more of her recordings. I'm sure she'd be the first to say it's not quite the same as Monk's great take on record, so nothing but praise. How many people would even try, you know? Good on her.