Not sure how well this would work, but someone I used to talk to used this same technique to record some anime for me years ago.
You could try getting a DVD Recorder (I've seen some at around $75 at Walmart once) and hooking it up to the same TV as the VHS recorder, then popping in a blank disc (must be DVD-R or DVD-RW) in the DVD Recorder and putting in the VHS containing the episode in the VHS Player. Then you can press play on the VHS Player a little before the start of the episode, and then on the DVD Recorder, press record.
If done right it should record the episode on the blank DVD.
I hope I didn't confuse anyone. ^^;