The low µv sensitivity of receivers is for a small bandwidth - your circuit is large bandwidth and thus will see higher levels, unless you go to very remote areas. A little more adjustment to gain might be needed, e.g. a switch to chose a factor of 10.
There is no need to spread the gain over so many OPs. As the output BW is low a single OP is good enough.
More OP only increase current consumption and chances for unwanted oscillations. The single OP version often also include offset trimming pins - so you could use these.
A little smoothing cap after the diode is a good idea, to keep the RF away from the OP(s).
Since this will be sitting on a coffee table, with a small antenna, and one constructed to simply add to the "mysterious factor" of the contraption, I see the added gain as a plus, but I am looking for ideas in how to implement a suitable gain control to manage it. Having gain which is not needed, but can simply be dialed up when needed appeals to me. I live in a semi-rural area, and escape much of the rf pollution of the city, so will scale back the amplification factor if it is found to be a problem. But, I would prefer to simply have a gain control which could deal with the problem nicely. And, since this is not a real measurement device, demanding any real accuracy, the noise introduced by the added stages will probably go largely unnoticed.
My junk box determined what I used, and the TLC274s were left over from another project of my sons, and I am anxious to be rid of one of them here, plus they boast extremely high input impedance, and will load the input ever so slightly -- the best in my limited junkbox (either this, or a LM324.) And, since it is a quad, I simply used them all, saving me from having to tie their pins to ground, to stop any unwanted oscillations. But, I am looking for ideas on how to implement a suitable external bias control.
Since the device will be operated from lithium rechargeable batteries, recharged by solar from light coming though a window in the afternoon, and the small solar panel simply adding to the devices "mysterious factor", and having line power at its disposal for sunless days, the power consumption of the extra few milliamps is of no real concern here -- its main power source being 2 x 18650 lithium batteries, it should be able to run for many days before there is ever a danger of running short on power, and the battery protection circuit kicks in to prevent a over-discharge which would ruin the batteries, given that the sun is not shining, and grid has gone down.
The cap will be experimented with, to see its affects, and whether they are desirable, or not, at the breadboard stage. No sense in having the rf bleed hamper the amp factor, if that is found to be a problem, correct, your caution will be implemented.