I'd add my voice to the 'I think the romanceNPC dialogue handles it well enough'. If this is seriously being considered, and I hope that it isn't, I think a stat check is in order. Can the PC get out of it in the first place?
Phaere actually does force the PC and there is no 'I don't want to' option without recrimination; the 'I can't' option checks stats as well, does it not?
That depends on what you say after that. If you say, "I'm a eunuch," or, "I took a vow," or, "I'm under a curse," that checks stats. If you say, "I belong to another, someone you don't know," that always works.
If you refuse, the city goes hostile and the eggs are lost.
Yes to the former, no to the latter--if you refuse, you just have to fight your way to the temple and seize the eggs by force. This is well within the abilities of the average PC. Whether it's reasonable to expect a PC to maintain fidelity in the face of blown cover and a huge battle is of course another debate.
A cleric of Talos, for instance, shouldn't incure a virture drop.. if anything it should increase - aren't they being true to their faith?
A cleric of Talos whose Virtue rises moves closer to Falling, closer to pissing off his most recommended traveling companions, and generally away from everywhere he would want to be.