Which ARM Cortex M chips allow for execution from RAM?
I know that some Cortex-M chips can run from RAM, but I've heard that this is not universal. 


You heard wrong. All Cortex-M chips can execute code from RAM addresses and from off-chip external ram should they support an external memory controller.

Only the interrupt vector table has a few more restrictions, which require you to put that table into on-chip ram or flash - see VTOR register description.

Note: Memory maps which describe where code is executable can be found in the coresponding ARM Architexture Reference Manual.