beigledog, personally I think the best negotiation tactic is to make an offer, skip the letter (although it is nicely written). As a seller I would take it as a sign of weakness on your part and would stand my ground firmer because of it. Never show the seller that you really want something. You also are insulting them by telling them how much work is needed and the state of the appliances. Gee, you guys lived in a house with some real crap, but now we want to replace all that and have you pay for it!
Submit the offer, show them that you have the money and are prepared for a fast close. And if they don't bite, wait them out. As Lentinman will prove to you, the inventory will be growing and many more houses will show up. It is your first buy, be patient, don't make the mistake of being overeager.
Signatures are so yesterday!