Wish I were there to help you troubleshoot it. The reason that I laid out all the steps the way that I did rather than just jump to the punch line was to help you troubleshoot the problem yourself. You did mention that you were able to get it to work just fine with coax through VCR1. But, did you try the next step of running it through VCR2 without VCR1? The reason I put this step in was just in case you have a bad VCR. I have a VCR that was struck by lightning several years ago. When it is on, it works fine. When it is off, it blocks the throughput signal.
Make sure that both VCRs and the TV are tuned to channel 3 when on. You may also want to check around on the VCRs for a switch that would allow you to toggle this setting between channel 3 and channel 4. It should be a small physical switch usually located on the back near the inputs. Make sure it is set to CH 3.
Unless your TV blue-screens when it gets snow, a blue screen is an indication that at least one of your VCRs was on, but tuned to a station that was snow. It blue-screened you to keep you from getting static blasting through the speakers.
The way you mentioned hooking it up with composite could work. Then you would have to switch the TV input from channel 3 to Input 'X' when you wanted to use the VCRs. But this would still leave you unable to record TV, unless you solved your original problem. Also, sometimes the composite cables do not allow throughput, meaning they block the signal when the VCR is off. You can try it. It won't hurt anything. But you might still run into some of the same issues.
(Looks like I was slow on the draw and you've already found a workable solution. Maybe next time.)