Since the political party does not "manufacturer" the signs, the "party that manufactured them" would be the printers.

The signs are the responsibility of the individual candidate, not the printer, and not the party. This is why every (legally) placed sign in a public way has the candidates name and contact, or that of their campaign treasurer, in small print on the bottom, either handwritten or a sticker. With the date the sign was placed.

It is the candidate that designs, contracts with a printer and pays for the signs. It is the candidate that places them or has them placed with their campaign staff and volunteers. The only thing the political party has to do with them is provide a central point of distribution for the candidates to supply campaign material.

Yes, I do know how this is done because I'm involved with it at my municipal and county levels, with both individual candidates and the political party.

You have the right idea, you're just specifying the wrong target,