If the cam is totally dry, the rubbing block can wear enough to spoil the gap/timing in less than 100 miles.

BTDT, a loong time ago. The engine ran (more or less) at speed, but refused to idle and was very hard to start.

If the cam is totally dry, the rubbing block can wear enough to spoil the gap/timing in less than 100 miles.

That's what I guessed.

Mine is greased and was when I changed points before firing her the first time. The gap seems to be holding nicely.

No.
Cannot be.
If you REALLY had "no spark", as in, tested at the plugs and nothing, you could turn the distributor 180 degrees and the level of spark would not change one bit.

If, however, you THOUGHT you had no spark, but didn't actually test it, maybe.

Generally, advance or retarded spark won't cause a sudden "no start" UNLESS you are so far off you have fouled the plugs.

If you really had no spark, but moving the distributor gave you spark, three basic things:

Distributor grounding (confirmable with a ground wire from dist. housing to block), a break in the primary feed from the coil (twisting the distributor gives a go, and then no-go condition), or a massive break in the HV secondary wire from coil to cap.

Three points well worth checking out to make sure that you don't have a no start when you least need it to happen.

I guess that the grounding could be true. The other two seem fine. I was unable to get the static timing right, as I couldn't get the light to go out when I turned the dizzy. This would seem to say that the ground was OK but the points weren't opening, however I watched them move as I turned the fan and checked the gap. That's when I gave up and turned the dizzy while cranking and it started right up.

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.