FWIW I have to put in my $.02. First let me qualify that I am not familiar with the MGB. After reading this entire thread, it seems to me the issue is most likely ignition related. Lets assume the fuel pump is providing adequate fuel which JB says it is and would further be evidenced by the strong fuel smell. The carb must have been working fairly well to pass the emissions testing, and aside from some catastrophic failure such as the needle no longer working or a huge intake of dirt they just don't fail that quickly. It appears the most recent issue was antifreeze in the distributor. I would want to look strongly at the condition of the points file and clean them as Dr. E suggested. Instead of a paper towel and alcohol to clean them after filing I always use a buisness card. Dampen it with alcohol (no rum) and swipe through the points. There is less chance of getting lint between the points. The next place I would look would be for a carbon track on the distributor cap or most likely the rotor. With all that antifreeze in there it would seem very likely to me that a track has formed from the rotor tip to the shaft which is shunting a portion of your spark to ground. Alternatively you could have a track in the cap which is causing a misfire between cylinders. I would think if this was the case you would be able to run, but it would be rough. I am suggesting that the starting fluid is able to burn with the weak spark but not the fuel. If this has been getting worse, then you would likely be smelling unburnt fuel while idling. The quick check would be to replace the cap and rotor (the ones you saved from the last tune up would work for a test).
Of course it could also be the capacitor, coil, secondary wires, plugs, primary wiring, rust in fuel tank, plugged fuel filter, plugged fuel line, vapor lock, cracked fuel line, vacumn leak, blown head gasket, cracked head, stuck float needle, leaky float, weak fuel pump, strong fuel pump, float level too high, float level too low, plugged exhaust and something else we missed.
Regardless of what the underlying issue might be I would suggest you have it identified before changing carbs. There is nothing worse than throwing another variable into an issue like this.
I hope that one more possible solution doesn't muddy things up to much.
BTW you might invest in a remote starter button. They don't cost much or are easy to make. This will allow you to crank the engine from under the hood and makes trouble shooting and adjustments much easier.
Regards,
Jeff