Well, probe and see where the currents are asymmetrical. Note that if you use the mirror, it is shorting out your one Q's compensation network, about as badly as with the collector tied to Vdd. If you make the input Z of the mirror high you lose signal swing, and you'll never get it up to the Z of the output node. For true symmetry and those R-C networks, you also must have equal voltage gains at each collector, since Miller strongly affects. Right now the left-hand one is not doing much.
I'd throw some R's in Q4-Q5 emitters for flexibility too.
See what the actual collector currents are for the two overload conditions at Q5. Maybe it is mainly a balancing problem based on the actual Q6 vs. Q7 magnitudes---after all, it doesn't take much to produce the mismatch reported.
EDIT: Actually the main problem is the response of the current source Q6, to the substantially greater voltage swing at the emitter of Q5 during the fall time. The nominal 5.924mA drops to 3.74mA for the duration of the slew event. This is about enough to account for the asymmetry I think.
You need a better current source, and maybe a bit of reduced swing on the bases of Q4 Q5---enough to fully switch. Maybe stiffen the impedance at the Q6 base too.
Actually there is a large asymmetry on the differential voltage at R3 R4. This is not helping. I think it's mostly to do with the large Miller effect at the base of Q5.
Further edit:
If you make the swing at Q4 significant by loading it with a large R (20k-ish) and feed its collector current from another 4403 (ground the 20k) you now symmetrize things much better, diffrential swings at R3-R4 are nearly equal, and the slew rate magnitudes are much closer. Both are a bit slower. So although not probably optimal at least it can be fixed.
I would probably find an alternate place to do the compensation that was inherently symmetrical, which probably entails a more inherently symmetrical topology as well.