I'm having a similar problem with my GT6. There was no spark, so I spent a couple weekends replacing the entire ignition system, excepting the distributor itself. Now there is spark (or at least power going to the HT leads for the spark plugs, I couldn't get the plugs themselves to spark, but I think that's a grounding issue, since I replaced them only a couple months ago and they don't look fouled), but no go.
Last weekend I finally decided to take a look at the timing and found that the vacuum advance mechanism had somehow become stuck in its full on position, and that on top of that the timing seems generally mucked up. The car is dead a good hour's bus ride from my house, so I'm going to head up there come Friday hoping that tearing down, lubricating and refitting the distributor will fix it.
I'm unfamiliar with the distributors on the TR3s, and I imagine yours has been rather better maintained than mine (its a new acquisition, and the previous owners seem to have been completely unfamiliar with the concept of lubricants),but as far as I know you should have a vacuum advance, so that might be something to check. I imagine that a faulty advance system in conjunction with advanced timing would cause something like the problems you've got, and if the vacuum advance switches back to its regular position, the timing will be thrown off again.