If "shadow invar" means "shadow mask", then it refers to the black pattern used to makes dots on the screen. Instead of using a mask with invidivual "holes" for the dots, the Sony Trinitrons use a grille of very fine vertical wires to separate red, green and blue dots. On large tubes the grille probably allows a bit more light through giving the Sonys a slight contrast advantage. And from what I've read, Sony's grille is a bit more durable than shadow masks. The masks have a little softer appearance though which is a bit easier on my eyes. I went with the Sony anyway though, because I wanted something that could withstand alot of abuse and customization.
I am a JVC fan, at least in terms of the picture, so your remarks don't surprise me. But I have no idea how they are on the reliability/service side. Sonys have a signature look which isn't everyone's cup of tea. It's possible to undo some of it though if you know what you're doing, or can hire a professional to calibrate it. IAC, make sure you're doing a fair comparison, the same kind of signals etc. And try the different picture modes on the TVs before you decide.
