It worked. My 513 took 727V after previously updating the firmware to 727H. It now has the ability to set title names in the timer record menu and it added the skip feature. I'm very happy.
Thanks Bizarro_Stormy and wajo!
1. The 727V update took away the "Reset All" option from the bottom of the General Settings menu (just like the 515).
2. The 727V update changed my 513's model name to E2S02
UD. Skip 123 F/W Version screen pic here
3. HDMI Control has been renamed fun-Link (HDMI CEC)
4. Skip Once feature now available in timer record menu.
5. Edit Title Name now available in timer record menu.
I ran it through a bunch of tests and it did everything correctly. HDMI Control (fun-Link) works. The tuner works as before. I did timer recordings, real time recordings, real time dubs, high speed dubs, timer record title naming, scene delete and chapter mark edits, thumbnail pic changes, disc finalize and un-finalize, dubbing and playback on a 515 from the DVD created on the V513. I don't know what else to test. The V513 seems to operate exactly the same as my 515. I'll call it a success.