I think you will get better results with a bipolar transistor in place of the FET because of greater transconductance. This also avoids the problem of trying to find a low threshold voltage FET.
I would consider the two transistor cascode amplifier for each stage to make the best use of available gain.
Using tuned circuits for the loads instead of resistors will also make the best use of the available voltage and current. The Q of of each tuned load will need to be compatible with the expected bandwidth to preserve the modulation.
Your requirements may be unrealistic. The best single transistor 32kHz crystal oscillators operate at about that level of current.
I agree.
People with little experience of Radio Receiver design often underestimate the pitfalls involved.
The most likely result is a device lacking in both selectivity & sensitivity, although the OP's spec of 100uv sensitivity is not very ambitious, so that possibly may be obtainable with a plain old "Crystal Set".'
Selectivity is another question, as there are the twin problems of adjacent channel rejection, & obtaining sufficient bandwidth at 125kHz to preserve the modulation.
Cross modulation from high power MF AM Broadcast transmissions is another likely trap, not to mention that from SMPS.
The dynamic range of a receiver operating on voltages of the order of 3.6v is unlikely to be able to handle interference from even quite distant lightning strikes, either.
Receivers used professionally at such frequencies are normally complex devices because of these bugbears.
Superheterodyne receivers can do this sort of job "standing on their heads", because they do not have to rely on just a few tuned stages.
SDRs can achieve similar (but, in my opinion, not equal results).
The trade off, of course, with such devices, is that they need much greater power to achieve their purposes.
Yes, OP, you are pretty much "on the road to Hell"!