You know what? I'm going to jump in here. I commend your concept Johan.
Couple of problems. Since you wish to amplify what you have, surely a 'hotter' LNA probably could be fashioned.
Analog Devices has a lot of developer board LNA's ready to go. Even the Gerber files to piece together your own incantation. As far as degrees kelvin versus dB gain, snr. That's your baby.
Unless the subreflector were redesigned into a different geometry or perhaps a multi faceted arrangement.
Each individual parabolic antenna is its own parabola. Combining many to focus in one spot. Not sure if that exists.
Like the James Webb and other telescopes. Each individual mirror is part of a single unit. A larger parabola.
If each mirror were its own parabola. It couldn't work. For optics anyway.
Dishes don't normally have long focal lengths. Try it with a stack of magnifying make-up or bathroom mirrors and see how difficult it would be to arrange them and focus the sun in a single spot on paper.
Different results if you were to have a large mirror and cut it into facets and separate them. The parabola curve would seem to me to carry on and be manageable if you spread them out. Dimples on a golf ball comes to mind. A bit hard if not impossible to get a smooth curve out of them if you cut them out individually.
Microwaves are nuts. Even the smallest deviation in alignment of multiple collected signals would send the antenna out of phase and subtract signal. Haha. "Mr. Heterodyne" still exists in everything RF to this day.