Just buy rods or a sheet then. Your plugs are so small anyway, as you said you could use them for plates or whatever be for other parts would be the easiest as the other guy said. Lots of reputable builders especially up north of the USA that you could ask to build you a small sheet in the USA
FYI and if it were me ( I dont live in the USA ), and you wanted to lay up a whole sheet in your garage without pre preg then you could layup 5 layers at a time with a vac bag, drop the temperature, pull the peel ply off while its slightly cured keeping a bstage, repeat the process so you getting a better crosslink with more layers with the same bag until your thickness you need and ramp up your heat on the final layup for the postcure to not get thermal runaway if you really wanted to get similar results to an autoclave with prepreg. Dont use any fillers and the same resin system to not get expansion.
Teds advice is anyways fine whether you build a sheet, buy a sheet or whatever, I would just use a proper glue like spabond to more or less match the carbon, push in as far as i could with a sacrifical little stopper at the back to try get some glue on the inside to help.
That is just what I would do, then again, Teds advice is the one you should be listening to here.
Good luck