I agree, I've never seen any restrictions on doing an onboard upgrade for a Weekly Special ticket. One cannot do the upgrade prior to departure, that is indeed blocked.

Back a few years ago when Amtrak was selling some coach tickets via eBay, those tickets did indeed carry a restriction prohibiting all upgrades including onboard upgrades.

All that said, as you noted, it can sometimes be an interesting exercise trying to get a conductor to actually do the upgrade. One tip that I can provide is to seek out a sleeping car attendant if you can and speak with them. Since many of them are interested in increasing their tips, they'll push the conductor harder to get that upgrade done. And the conductor can't tell them that the sleepers are sold out when they aren't, since of course the attendant knows how many rooms are occupied.