Really nothing new here. The use of magazines/magazine base plates with firearms with mag wells has always been iffy, regardless of the firearm manufacturer. This exact same thing happened a few years back with Sig's P320 series. Sig's model with the mag well had rounded base plates on it's magazines to fit the magwell, but most other Sig magazines had squared corners and wouldn't work.
In the case of the Competitor, it was supposedly designed with using it for competition shooting, so naturally a mag well is part of the package. Unfortunately that just opens up the probability that all magazines with base plates not specifically designed for use in that pistol are not going to work.
About the only solution is to remove the mag well, modify the base plate so that it does fit, replace the mag base with one that will fit, or install a bigger aftermarket mag well that will accommodate the larger base plates.