Mike,
EL and TF are the correct prefixes for a 1928-1931 Douglas Dirt Track (DT) or Speed Way (SW) machine. The London Douglas Motor Cycle Club has a machine register for all Douglas Models, and it shows fifty-eight DT/SW models, but far many more survive unlisted. It is felt some 2800 were made in the four years. The DT and SW were very similar, the SW having a flywheel clutch, brakes, mudguards, etc. They were 500cc, but could be had in 600 and 750cc by changing barrels and heads. About 1929 they change from a tall airbox to a small square one that incorporated a mechanical oil pump.
Many DT machines were converted to grass track racing when they became uncompetitive on the cinders. Those that survived that were often converted to SW specifications to extend there useful careers on the road as vintage motorcycling became more popular. Today the only place the old fore and aft Dougies still seriously compete is in the vintage sprints (though not with the hand change Douglas gearbox.) And of course in the concourse arena. There are some Dougies still doing demonstration cinder track runs in the UK, as an exhibition during a modern race event.
The engine, trans, and frame numbers would not match from the factory. Engines were built in small batches in the experimental shop then sent out to assembly area be mated up with trans/frames. Likewise transmissions would be built in batch lots in the assembly areas. The numbers ought to be within several hundred of each other, but by this day and age it would be surprising if one or another major component had not been replaced, particularly on a competition machine. The Douglas o.h.v. engines go like a bomb, both when running and when they inevitably blow up!
The DT/SW models Achilles heel is the crankshaft. Rebuilding options are very limited, and good used ones are carefully hoarded, replacements non-existent. The problem is the crankpin surfaces begin to brinell, and bits flake away. The crankpins are integral to the two-throw crank and re-grinding- besides cutting through the case hardened surface of the pins- prevents assembly! Also one should inspect for cracks around the drive side crank case main bearing boss, a known area for fatigue.
Unless the providence is rock-solid, ownership by famous Dirt Track personages like Fay Taylor, Sprouts Elder, or the American hill climb ace Reggie Pink are viewed with initial skepticism. It is the old story, everyone had a DT that was raced by so and so. And several are already attributed to Fay Taylor I understand. That is not to say it can not be one of her machines; as with many famous racers she would have had several machines during her career.
I am reasonably familiar with the mechanical aspects of these models, so if you run into more questions just ask.
-Doug