If I read the Wikipedia article on the Motorola 6800 correctly the 6802 and 6801 share the same CPU. You might check the 6502 out as I believe it was intended to be pin-compatible with the 6800.
The 6802 is a 6800 with a different hardware interface (clock & power) that is easier to design for and results in cheaper designs. It is 100% compatible with 6800 software.
The 6800 does not support stack based languages like C well.
There was a Flex small C compiler, but I think it generated bytecodes that ran on an interpreter.
It's still pretty fast but I'm not sure it's fast enough for your application without at least some assembly code to support it.
The 6801/6803/68701 are all microcontrollers with the same CPU core plus some built in hardware. They run 6800 code but have built in hardware addressed in the first 16 bytes of the memory map.
The 6801 has built in ROM companies could order preprogrammed with their software.
The 6803 either has no ROM or had it disabled.
They all have some built in memory, but I think the 68701 had more than the other two.
There are several different DIP packages for these chips but none are not pin compatible with the 6800 or 6802. If the buss/clock interface is similar, then they could be adapted to replace the 6802, but I don't know off the top of my head.
The instruction set has been enhanced over the 6800 with a multiply, Add B to X, A&B registers can be combined to form a 16 bit D register, and many opcodes require fewer clock cycles.
Hitachi offers even faster/lower power versions of these chips (HD6303). Many opcodes execute in fewer clock cycles. All single byte opcodes that operate on a single register require 1 clock cycle. The multiply is 3 clock cycles faster than the 6801. It adds an eXchanGe D & X instruction and some bit test instructions.
The 6803 is easier to program than the 6800 and most code is smaller.
There have been commercial C compilers that supposedly support these CPU's, but I've never gotten ahold of any of them.