Re: Vintage trem has a slight issue
I used to love a vintage trem but always had the best luck having the trem rest against the body. The last vintage trem I had stayed in tune perfectly as long as I had it resting against the body. They were not designed to be floating trems like the 2-point design. Even the 2-point trems can have some tuning stability issues once in a while. Such is the life of a trem. However, you can do a few things:
1. How is your setup?
2. Is your spring tension too tight or not tight enough? (If your bridge is getting pulled towards the body then spring tension might be too tight)
3. Do you have a graphite nut or do you use some kind of nut lube on the nut and saddles to keep things moving freely?
4. When putting on a fresh set of strings, do you work them into place by stretching them via the trem? I like to push the trem down a few times a bit to stretch them out, then re-tune, do it again, re-tune and one more time. This seems to help.
As far as getting your vintage trem to stay in tune while trying to keep it floating goes, well, I tried for years and years with no such luck. I eventually caved in and set it against the body which gave me some of the best tuning stability I have ever had on a vintage trem plus more sustain.