Er, no, what I mentioned was 3.45 (at least that's what I meant to mention, might have fumble-fingered). In my case, that will just about compensate for my shorter tires, leaving me with an overall ratio close to stock. 3.45 was the stock ratio for some big Triumphs (like the PI TR6) and those gears will fit the TR3 housing.
There are shorter ratios available, though. When I got the car, it had 4.10 gears and no overdrive. With stock height tires, that would have put me at nearly 4000 rpm at 70 mph. (With the tires I use, it becomes roughly 4200 rpm). The engine still makes plenty of power at that rpm, but it's kind of like driving around in 3rd gear all the time. Try it, I don't think you'll like it.
Most LBC vendors can get the 4.10 gears. TRF has them listed as in-stock (PN 505014). 4.3 and 4.55 gear sets are also available (from other sources), but simply absurd in a TR3, IMO.
In theory, the shorter gears give you better acceleration from a standing start. In practice, though, you wind up having more of the engine's torque go into accelerating the crankshaft and flywheel, so the improvement in acceleration is quite a bit less than the theory. Steve Hedke did some careful measurements with Scrappy (the TR3 he ran in The Great Race) and found that he actually got better acceleration at part throttle with the 3.45 gears (and stock tires). (The Great Race is a TSD event, so it's all about repeatability rather than all-out performance.)
My opinion, a lightweight flywheel is much more "bang for the buck".