8051 MCU with fast entry to ISR implementation
So, I'd actually recommend Cortex-M0 for the reasons that you cite against Atmega:

The Cortex-M0 microarchitecture is pretty smart when it comes to helping developers implement real-time OSes. For example, pushing registers is done for you (of course, limited to the relevant registers, and I'd guess that's where the latency comes from), and the hardware handles two different stack pointers, depending on whether you're in "application" or "handler" mode.
 I'd like to refer you to the presentation Mr. Moritz Fischer held at FOSDEM 2018 about Multitasking on Cortex-M.

Bonus (but my guess would be the STM8 has something like that, too): Cortex-M0s typically come with capable DMA engines linked to their peripherals. If you, for example, need to bitbang a pin with a sequence of 128 hi/lo states, you can just let the peripheral do that. No need to interfere yourself, just write the data to the right position, and inform the device or dma controller what to do. The capabilities of course depend on the actual peripherals that the silicon manufacturer (ST, NXP, Atmel, Cypress…) attached to the ARM core. 

There's several ready-to-use free RTOSes for Cortex-M. So, that might be a reason to use that – especially if you prefer C over assembler.

I've not tried these, but: The Cypress PSoC 4200 series comes with what they call "programmable universal digital blocks". These things are meant to be "independent" hardware state machines. Pretty much exactly what you need to implement wire protocols.