Ed,
Good going!
To get a good starting point on the rich running, turn in the jet adjusting nuts all the way in, counting the number of flats (each nut has 8 flat edges). Then back each one out 12 flats. This is only a starting point. Then mark the flat of each nut at the same place on each carb with a dab of paint for your reference.Now turn in each carb nut, counting the number of flats you turn it in) until the carb leans out. The procedure for checking involves lifting the piston lifting pin and listening to rpm increase or decreases. This gives you an indication of lean or rich. I don't have my cheat sheet handy and don't remember which is which but someone will chime in with the detail. Between each test lift, rev the engine and let it settle back down to idle rpm.
I hate to tell you this but to tune the carbs, it is assumed that the dwell and timing are correct and that the engine is up to operating temperature. So you might want to continue with the timing first. I would turn the advance knob on your distributor a couple of marks towards advance. I only suggest this because 1) your car is still popping a little (indicated retarded advance) and 2) a retarded timing can cause a rich running condition. Use a timing light an observe the hash marks that the previous owner put on the pulley as your car idles and also as you increase the rpm. If the marks don't move as you increase the rpm, your vacuum advance isn't working - could be perforated, corroded, or just crapped up where it attaches to the distributor. If the advance knob doesn't make a difference, mark the distributor position on the clamp and turn it just a tad. Then use your timing light to verify your change.
Also, if you need, I can scan a cheat sheet for timing and carb adjustment and email it to you. Just remember, now that it's finally running, to mark the currect settings before making any change. And if the change makes no difference, put it back.
Keep us informed. Everybody wants to see you car haul. The TR3 is alot of fun to drive and hauls butt when you get it tuned correctly.