Padauk makes them (or at least did), and calls them FPPAs. These are the same folks that brought you those infamous 3-cent-at-single-quantities OTP microcontrollers, so they're probably not for the faint of heart, but what you're asking for has been done.

Some of those 3 cent microcontrollers are actually barrel processors! They have multiple sets of registers (only two on the cheapest) and rotate through them with each clock. Useful for implementing an SPI or UART thread alongside the main task, for example.

The SDCC open source C compiler targets some of those chips now, too.