Doc is way fun...
I only had a chance to play around with Doc against CPUs tonight, so take this with a spoonful of salt:
Despite you efforts to avoid the Melee problem of Doc outclassing most of Mario's game, it seems like in the end that's what happened.
Combos - Doc's combos are different than Mario's, but at least as good... possibly better. As you demonstrated, bair to grab is nifty, and Uair combos like gold until previously unheard of (for Mario) percents. The u-tilt and the dair don't have as much combo potential, true, but the core of his combo game, Uair and d-throw overshadow these slight loses. Also, dash attack is nuts. Since it makes you trip you can do pretty much anything out of it, including grab, d-throw, continue combo.
Recovery - We're stilling planing on nerfing Doc's cape's recovery a little with the help of Almas's custom gravity code at some point. Still, his recovery isn't terribly worse thanks to the increases in jump height.
Killing - Doc's killing options seem to require mostly higher percents than Mario, but they're more consistent and easy to land, which I think ultimately becomes more important. Mario's f-smash killed many characters around 90-something depending on stage location and DI, but it required you to usually mindgame into it a little due to it's start up time -- Doc's comes out fast and is balanced with low range, killing at higher percents. Overall this move is fine. D-throw to Fair is a pretty awesome killer, though, and the KB of his Up-B in the air made for some rather low percent ceiling kills (106% on Peach middle of the screen), although this is probably mostly due to a lack of DI. Overall I actually prefer Doc's KO options (>.<)
Gimping - Bair >> FLUDD, in my opinion. The Fair was a mediocre meteor at best, and its loss isn't too significant. The larger cape size also helps in staying safe while taking out recoveries.
Projectiles - 8% semi-spiking Darkness Ball >>> Normal Fireball, obviously. I know we want to change this.
Right now I just don't see a ton of reason to use Mario, other than some alternative combo options, a sliiiiighly better recovery, and the chance to mindgame your way into some stronger (but much more situational) kill moves.
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Here are some changes I'd like to see:
-Uair -- 8 or 9 damage from 11 (adjust KB to be the same as before)
-Bair -- 9 damage from 12 (adjust KB to be the same as before)
-If you really don't want to decrease these damages, then you need to lower the KBG of the Fair
-F-smash +5ish frames of cooldown for sure, maybe change it to 3 frames removed from startup
-The 60% ALR is barely noticeable, maybe increase this to 70%
-Fair needs it's SFX changed to something a lot meatier
-Lower Up-B's KB on last hit a little
-The dash attack's actual downwards KB is too strong. A Lucas at 35ish percent was hit with it at the ledge and dropped just past the bottom of FD before he could Up-B. Also, the dash attack might let you infinitely trip them on the stage, possibly requiring more cooldown.
-I dunno if the >100% ledge attack needs to trip.
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The theme of the feedback is that in your plan the main thing Doc was supposed to sacrifice was KO power, and some recovery. I don't think that his KO power is weakened at all, and you yourself said that it's better "in his own way." It's more consistent, which I find better, and in some cases actually lower than many of his old options (Up-B?) The recovery, even with the eventual cape nerf won't be too much worse. Thus, he either needs to give up some damage, or give up more KO power.
We'll talk about this on IRC sometime tomorrow.