Strange Problem

I am seriously considering buying another S-10 with a 4.3 engine and manual transmission and retrofitting it with a carburetor and HEI ignition

Why stop there? A 350 will fit in there with a little remodeling and then you’ll have some real fun.

As to the original poster, it would appear to have all the hallmarks of a failing BCM, easily diagnosed with the proper scan tool hooked up during time of failure. A loose intermittent ground or data wire could also be possible.

TIPM does cause the problem the OP describes and OP does have a TIPM. The NHTSA is broadening it investigation The problems affect the entire vehicle including, but not limited to engine dying.
http://www-odi.nhtsa.dot.gov/cars/problems/defect/results.cfm?action_number=DP14004&SearchType=QuickSearch&summary=true