So while siege is the idea that's brought to mind, I did think about your questions while writing.
I don't think anything should be diplomatically impossible. If you make the opportunity cost sufficiently high then it means people won't go for an option. E.g. "Request Cardassians join The Federation" - the process for this wouldn't be just a 5 year stint, however. This would mean 15-20 years of long negotiations, perhaps. 15-20 years which could be better spent doing something else, like improving your relations first.
I agree with inspi (I think I met you through MS? [I'm Max]) about the idea of benefit being a determiner in length of negotiation.
At first I thought this would be a good way to specifically limit player to AI interactions, but I'm not a fan of features that don't work the same for everyone. In particular, though, I think the player being forced into decisions they might not make themselves would be fascinating. After all, you're the spirit of the country and there are plenty of events that demonstrate things beyond your control.
Loss of stability for rejecting ambassadors - or perhaps even the cost of your own ambassador to stop such negotiations could be interesting. Though at what point would the AI use a strict reject for that to be fair?