You are correct, you cannot put a plate amp into this horn. I don't know what 'most' people do, but I have seen several build threads where people building tapped horns built a separate box for a plate amp. Then they run the wires from the plate amp box to the horn just like you would with a rack mounted amplifier.
Now that you mention it, I don't remember where they actually put the amp boxes in their setup.
Where are you putting the horns? If you put the amp in a box and finish it like the horn cabinet, you could probably put it on top of the horn.