Here's the scoop. Japanese and Squier VM offset hardware is usable but you have no guarantee that the bridges and trems they use are manufactured with low tolerances or margins for error. They’re pretty bad.
An AVRI/AV bridge is considerably heavier and with a little nail polish to the screws before setup should be a dream to play. Vintage American hardware doesn’t even need nail polish a lot of the time and I suspect that earlier AVRI models don’t either. You know, when the tooling is still fresh, etc.
Also take into account that Jazzmasters and Jaguars don’t give a crap about what strings you like. They were designed for 11s or HEAVIER for standard tuning. You can make it work for lighter gauges, but that’s not what they were designed for. Remember, initially they were sold to jazzers and then to surf musicians. That's usually flatwound 12s or 13s.
Just follow how they were supposed to be set up in the 60s. The design is good but the circumstances around the construction will lead to your typical problems. You get what you pay for but there are workarounds.
Oh, and I still absolutely hate the TOM bridge on Jazzmasters and Jaguars that weren’t designed for it. If you have a CP or a Mascis, fine and dandy so long as you don’t abuse the trem but I’ll never understand the point of a TOM on a 7.25”.
