More and more, your description of the problem seems to line up with Super Eye's theory that one or more of the video circuits in your JVC have gone bad. You say the output gets "even darker when I turn the TBC on," which is the polar opposite of a properly functioning JVC: switching on the TBC/DNR should either increase brightness and color slightly, or not affect it at all (aside from clearing up color noise).
An external TBC used with your Mitsubishi may or may not fix the Mitsu's dropped frame issue. External TBCs behave unpredictably with VHS, they often help with drop frame issues during PC capture but they can also degrade the image slightly or notably: colors change, sharpness changes, brightness and contrast changes. Since you are very concerned about this, the only external TBC you should even remotely consider is the AVT-8710
, which is the only sub-$1000 TBC with user color adjustments (proc amp) built in. The controls are crude but something is better than nothing.
The "TBC" built into the JVC isn't the same as an external TBC: its more of an adjunct to the DNR circuitry, helping clean the video, smooth out noise and correct geometric distortion. External TBCs don't clean noise or correct geometric distortion, they just help with dropped frames and lipsync drift. The entire point of bothering with a twitchy pricey high-end JVC (or similar Panasonic or Mitsubishi) is this noise cleaning TBC/DNR feature, so if yours isn't working properly and the video output is objectively very defective, the unit is hosed. If you can't get a refund from the studio, try selling it as-is on eBay to someone who wants to deal with the repairs. You could get $50-$150 for a funky 9900.
All of the high-end VCRs combine this amazing TBC/DNR feature with lousy, unreliable transports and other electronics. Everyone tolerates the high price because the TBC/DNR is unique and invaluable for some tapes, but the underlying machines are generally much less well-made than the cheaper consumer models of the period. There are millions of Panasonic PV-4660s and JVC HR-S5912s still working perfectly, while the fancy AG1980s and HR-S9911s litter the video landscape in sad dysfunctional piles. They are a necessary evil for some of us, but require extremely careful shopping and buying. Always get at least a one week trial period, and test the hell out of it with a variety of tapes. Its also a good idea to to have a competent repair tech on speed dial.