I've never heard of an inedible plum before! If they're a bit on the sour side to eat fresh, make them into plum jam or plum pie (delicious!!).

Resin

I have seen edible red plum trees in an apartment landscaping in the high deserts of norther Nevada. These were quite good eating.

I have attempted to find one for my home and failed.

If, repeat if, you are into spending and experimenting I once heard an academic hypothesis that you could get some of the stuff made to cause all fruit on the trees in orchards to ripen at the same time. Then really overdose your tree back when it has tiny fruit, just after the blossoms drop. I tried it once on an apricot but run out of chemicals but I sort of feel it might have potential. From my experience I feel you need a really good sprayer and a lot of chemical.