Quantum TV v. Prior Recorded Shows

I have Verizon FIOS. I want to upgrade to Quantum. I have to turn in all my equipment and get new. BUT I want to watch all my recordings on my dvr box and not lose them. I have 89 recordings. Why can't I do this? The old equipment is not compatible with the new. I even asked if I could keep the old DVR box (and pay for it) until I watched the old recordings. Nope. There has to be a work around.

I read an older post that said I can keep the old dvr box and just plug into a new HDMI input - then switch between the two inputs until  have exhaustd my prior recordings.  Does this actually work?   Would old dvr box have to be hooked up to the coaxial?  Would it work just like an external DVR/Dvd player?    

I am sure someone else has this issue!!   TIA!