Well, about tempo, I think the 88 bpm is kind of a meh in between tempo. (Yes, I know that's where Cannon took it, but that's Cannonball Adderley and his group, they could make anything funky.)
For me, I'd either juice it up to around 120 (and this is where I would put it for a beginning improvisor), or I'd drop it down to around 72 and think of the Ray Charles band doing it. Thing is, at those low temps, you've got to stand on the back beat and lay way back from the beat, and you've got to have a rock solid rhythm section to support the horns laying way back. If you listen to Cannon's famous recorded version you'll hear just how far back the horns are off the beat.
OP, I think the reason your version doesn't do much is partly because of that meh tempo, but you need to use this tune as a lesson in how to be funky. Not just funky, but FONKEH.
The melody is dead simple. The chords are trivial - heck, there's only one chord for that whole first 8 bar vamp. What this tune has when correctly performed, is FONK. I would suggest that before you try to drape a few little noodles over the chords, you need to get some rhythm into the head. I would suggest you listen to several different top bands play this tune:
Basie, Buddy Rich, of course Cannon's group, Maceo Parker, jaco Pastorius, and James Brown!!! have all done versions of this. Note how these groups accent in the head. Note how when they stop a note they don't just let it die off like an expiring sparrow; they play a stopped note like this: DAAAHT!!. Here's another thing; when you've got a couple long notes where the second one's off the beat - like in the last 4 of the tune, you've got three eighths pickups and then two dotted quarters - put a little gap in between those two dotted quarters - it helps emphasize the off-off-beatness of the second dotted quarter.
Frankly, I've got the JB version in my head phones right now and I'd recommend that as an exercise in how to play this tune properly SLOW and FONKY. Imagine that you've got Bernard Purdy back there SOCKIN' the two and four. STAND on that two and four, baby. The backbeats are where the music is, in this style. If, OP, you choose to work this tune in the slow style, get yourself a backing track with a real backbeat, stand on those twos and fours, and try to lay back off the beat.
Until you learn how to put some FONK into the head, trying to noodle around on the changes is just wasting time in my opinion.
When you feel like the head is properly passionate and funky, then try to work up phrases that are just as funky as the head. If it just lies there going tweedle tweedle, don't play that one again.
Now I'm listening to the Brad Rambur/Eric Marienthal live version of the tune. Listen to the solos here. They are appropriate for the style. This ain't no bebop; this ain't no samba; this ain't no Lennie Tristano, this is funky-butt dance hall music.
The whole thing in all of jazz is RHYTHM and SOUND. No one really cares about the notes. Think of Ornette - heck, he'd play any notes he thought sounded interesting at the time - but he was always, always dead on with rhythm.
Once you get back into live playing, if your band leader says "tone it down, this isn't the Funky Butt Dance Hall" you can always play limper, but till then you need to model some real R&B sax playing for soloing on this tune. Remember -
Accents.
Rhythm.
Don't just let a note lie there, do something with it.
Rhythm.
How you stop the note is at least as important as how you start it.
Rhythm.
Have a distinctive sound quality.
Rhythm.
I'll leave you with this excellent example of phrasing on the head of this tune. It's not the only way to phrase it, but it's a damn good one. Try to duplicate this, then spread that whole feel out into a solo.
View: https://www.youtube.com/watch?v=oBi2xFqGKFc