Something sounds a bit odd here if it was incapable of a positive rate of climb on one engine.
Maybe the spare engine was in as bad a shape as the one that failed?
the captain being the owner of the airline,
Being the owner and chief pilot can be a dangerous combination. Commercial pressures to fly, even when you know there might be problems with the aircraft. Not an enviable position..
The Convair 340 was from an era that predated the terms FDR and CVR. Were they ever mandated? Otherwise, it was probably grandfathered.