Reading RAM externally in a running system by intercepting the memory bus or replacing the RAM chips?
Is it possible at all?


Well, maybe yes.


  Is it feasible to do this on commercially produced motherboards with
  soldered RAM chips found on consumer electronic devices?


Definitely no. Connecting wires to the lines between the CPU and the RAM without disturbing communications is extremely difficult. The faster the bus is, the more difficult this is. Replacing the RAM chips with something (a larger FPGA + external RAM would probably suffice) that "simulates" a RAM chip to the modified system and does whatever you want with the data is probably a lot more feasible. 


  Are there any off-the-shelf devices that can do this?


Most probably no.