To me its all depends on how much you want to accomodate the renter.
As for me, I send a rental agreement to the renter. If they accept the terms , which is 100% due upon receipt of official reservation in the renter's name, I'll send the official reservation in their name prior to payment being rendered.
I do this for two reasons, it does give the renter peace of mind and its no loss to me, becuase at least with Marriott there is no cost sto change names, so if renter changes their mind I just change the reservation with Marriott.
As for verifying ownership, that is something the renter should want to do because anything you send them can be forged. I give the Marriott customer service number to the renter and they can do the validation of ownership.
As for accepting partial payments, I used to, but find i no longer need to because I get so many offers. Just recently someone tried to low ball me and suggest staggered payment for a Maui 2012 week. I said no thanks price is firm and I require full payment. He said, "OK I'll take it"
Now if I was more desperate I would have considered his offer, but I wasn't. So you have to decide if you want to play cat and mouse considering April is not that far away.