It seems like it should be OK if the amount of correction is modest. IIRC it's something like 3 mV per dB of current difference so depending upon how many mV you need to correct the current imbalance in the long tailed pair won't be large enough to cause a huge asymmetry. There may be slight differences in max + slew rate vs max -slew etc, but conservative design, should provide adequate headroom, and negative feedback will keep everything in line.
FWIW, another way to skin the cat and keep input devices at same nominal current density involves resistive emitter degeneration with the servo current injected directly at emitters, but hanging servo resistors off the LTP will mess with input CMR if opamp used non-inverting, so tweaking elswhwere (like your first choice) might be preferable.
JR
EDIT? What do you mean by "tail" current, just one collector, or the common emitter drive? My answer is ASSuming you mean one collector's current.