My hunch here is that there is something wrong with the heatpump idea.
Solar powered heat pump
Heat pumps usually have a maximum coefficient of performance of about 4 - for every 1J of electricity, they can transfer 4J of heat. Solar panels usually have an efficiency of about 25%, for every 1J of sunlight, they can generate 0.25J of electricity. So for solar powered heat pumps, for every 1J of sunlight, you could get 1J of heat. I'm sure the problem is obvious - you could skip the solar panels and heat pump and just use concentrated sunlight to generate the heat.
Nuclear powered heat pump
The other viable energy source is nuclear, but a nuclear reactor already generates ample waste heat. I believe nuclear reactors are usually somewhere between 33% and 50% efficiency, so for every 1J of electricity, you get 1-2J of waste heat. That is low grade heat, and we want high grade heat here, so extracting high grade heat from the reactor will lower it's electrical output, but reduced efficiency is also what would happen if you take the reactor into to lower, hotter altitudes, the problem is cooling the reactor:
The bigger the temperature difference between the internal heat source and the external environment where the surplus heat is dumped, the more efficient is the process in achieving mechanical work – in this case, turning a generator. Hence the desirability of having a high temperature internally and a low temperature in the external environment.
The take home is you would be much better off designing the reactor to run at 50km, and extracting high grade heat directly from the reactor, this would dramatically simplify the setup, and probably still result in higher efficiency.
I think there are also other grounds on which this idea doesn't work, for one, the vertical altitude difference is about 10-12km, it is going to take energy to make that trip, for example it might involve compressing a lifting gas to cause the airship to descend. The problem is, that while heat pumps become more efficient with a hotter heat source, it wouldn't be clear that the energy expended in descending and then ascending 10-12km, wouldn't have been better spent just running a heat pump at an altitude of 50km.
The clincher is that if you are above the sulfuric cloud layer you get ample solar power during the day but if you are below the clouds you need to rely on either a nuclear reactor (already covered) or stored energy. But at least half the point of generating methane is as a means of energy storage, using stored energy to create more stored energy does not sound terribly efficient.
You're either going to have a nuclear reactor, which already provides ample high grade heat, or you're going to be using solar power and will be wanting to perform energy storage where energy is abundant above the cloud layer, which incidentally also provides an abundant source of high grade heat in the form of concentrated sunlight.