How far did you get with the FiOS and the DVDR?
I live in Southeastern PA and had FiOS connected on 9/15. I also have a DVDR-3575H with which I have been quite happy. I attempted to hook up the cable directly from the wall to the DVDR, as txrose suggested, and got nothing, i.e., no ability to scan channels coming in from the cable. All I can do is run the cable out of the cable box into the DVDR (coax all the way) and set the DVDR to channel 3. Then I get whatever the cable box (or, STB as its called) is set to. The STB needs to be set with the overly complex Verizon FiOS remote to whatever I want to record. HOWEVER, I don't want to record ANYTHING, because the PICTURE QUALITY the DVDR is getting from the STB (and subsequently sending to the TV) is atrocious. So, I'm not sure that the "splitter" idea will work for me, since my DVDR can read nothing from the cable without the STB intermediating.
I am now going to go to the lengthy thread (940657) to which txrose referred us and see if there are any options for me in there. I am leaning toward deciding that my best option is to cancel FiOS TV and put a FEW extra dollars into my Netflix subscription, and watch what I want without a lot of finagling.