I realise the problem with giving them away, anyone who wants to take a pet should be able to afford to care for that pet, and the costs associated with keeping an animal, and thus should not be put off by having to purchase the animal initally.
However, I also understand the points regarding the situation etc, if you for some reason, do need to give your animal away quite urgently, and you have a price-tag on that animal, then it may take longer than required to sell the animal. I'm sure most people will only give their animals to a fit and proper person and loving home, regardless of the persons financial scenario.
Maybe Tilly could offer some advice with regards doing checks etc, as she reguarly helps to re-home animals iirc? I tried PM'ing her but she is over her PM limit at present.