In newer vehicles with all the electronics under the hood, the symptoms you described of dieing thn starting up again 15 minutes later would point directly at a faulty electronic component. It's not unusual for electronic components to fail when hot, yet operate fine when cool. The heat causes things to expand and loose contacts to open. In your case, the most likely culprit would be the HEI conversion. Short of replacing it and seeing if that fixes the problem, I have no idea of how to check it.
I am completely nfamiliar with the Carter/Webber carbs you have installed; so, I won't go there as regards your running rich/burning oil? problem. Since you say the compression is okay, have you checked for oil in the coolant, coolant in the oil? The oil loss may not be related to the smoking. It is kinda' hard to distinguish between black and blue smoke. Have you replaced the spark plugs recently? What did they look like, how do they look now? This could help in determining if you are just running rich or burning oil as well. Of course if you are running rich, ignition problems could also be the source or at least contributing factor to the problem.
