Can we trade some efficiency to curb high-altitude emissions?
There's a fundamental problem. A jet engine performs work by expansion of the combustion products. Compressing the combustion products would require at least as much work as was provided by the expansion of the combustion products. Only an external combustion engine (for example, a steam engine) would work in this case.

A second problem is that the mass flow of the CO2 is more than three times higher than the mass flow of the fuel. Your plane would get heavier as you fly, and since the max landing weight of a typical plane is lower than the max takeoff weight, this will severely limit the aircraft range.

All in all, you can probably manage to make a purpose-built plane that fits the bill but I highly doubt it will have much usable payload if any at all.