And here we presented with the classic weakness of the 231 V6. GM put the pump at one end of the motor and the oil pan pickup at the other. Summarily, the oil has to travel from the pan to the pump, traversing the entire length of the motor to do so, before it can be introduced into the oil galleries and do some good to the rest of the motor.
My old 78 came with a 231. In the middle of winter, with straight weight heavy oil in the bucket, by the time the engine warmed up the oil light would come on. You could drive it and the light would go out but, as soon as you hit a red light and had to stop and idle, back that light would come. Unless you are married in church to the idea of keeping that V-6 boat anchor the best option is to scare up a donor and do an engine swap. From picture and your comments, what seems to be what you have is a Cutlass with that V-6. That being said, losing the stone and replacing it with an Olds motor is one possible option. Olds's ran a 307 V-8 which, from comments posted hereabouts, is sort of the default base motor but they also had 350 motors which weren't chevvies with phoney badging on them and grew from there to as big as 455 Cid big blocks. Depending on what part of the country you live in and how plentiful salvage and parts yards are, it might prove fairly easy to locate a score an Old big block for your ride c/w transmission. Some yards like to do the picking themselves; others will allow you to bring in tools and do the pulling and grunt work yourself.
Oh, yeah, for those who might wish to point out the abilities of the Turbo charged version of the 231 that Buicks ran, yes they were a fast ride but still possessed that flaw in the oiling system. I guess it is a mechanical iteration of the old phrase, "live fast, die young, and leave a rust free corpse."
Nick