The retard not working would certainly explain the high idle.
Although it's better to use instruments (vacuum gauge, Mityvac), you can get a good idea by putting your finger over the end of the tube to see if there is vacuum being supplied. It's not very strong, but if the tube wants to grab your finger at all, there is probably enough that it should work.
I'd also check that the plate inside the distributor can be moved by hand (compressing the retard capsule).
If the plate is free, and there is vacuum being supplied, the module must be bad. If so, you have to decide whether to tune without it, or get a new one (or try having yours rebuilt).
If you try to tune without it, and can't get the idle down, most likely the throttles are being propped open by the bowl vent valves. I'm not sure exactly what they look like on a 73 TR6, but on my 73? Stag carbs, there is an adjustment screw and a spring metal clip that it bears on. I had to pull the clip off and bend it to get enough adjustment. Apparently on later carbs, though, it was just a screw (Photo courtesy Nelson & Buckeye Triumphs).