The difference you hear is the ROSC pin is tied directly to ground on the new A4888 what set the off-time internally to 30 μs. This will give a more smooth sound and not so aggressive as the 10µs in the original setup.

This could be achieved just by a solder bridge - no need to replace the driver PCB!

BTW - to answer all these question mankind invented datasheets: https://www.pololu.com/file/0J450/A4988.pdf

I'll test the voltage, but I understand your stance that the drivers are likely providing appropriate current to the steppers.  Thanks for providing an empiric way to test that.

The only other thing I could think of that would explain shifts in the X and Y axis is that the octoprint server was creating those.  As you had previously suggested, I am now trying my prints from SD card, but those keep failing with SD card read errors!

On my board I've measure 1.32V on pin 17 - that is the reference voltage that controls the current limit! 3.3V gives 2A current that is the maximum current the A4988 can handle!

The formula to calulate the current is: I stepper = U ref / (8 x R sense) = 1.32V / (8 x 0.2ohms) = 0.825A !

The motor can handle 1A - so there should be no overheating at all!

I am going to bypass Octoprint server and use the SD card exclusively for the next several prints.

I just had a print shift 5 full centimeters toward the optical sensor on the x-axis, and about 1 mm toward the back of the bed.

It was printing strings all the way over to the end-stop sensor, and didn't seem to stop once it was at that sensor.

I'm pretty frustrated with this thing.

While printing, shouldn't something being placed in the path of the optical end-stop sensor do SOMETHING?

I've did some comparison between the steppers and the hottest is always the extruder stepper. On my machine it get about 50°C - the others are about 45°C.

As long as the drivers are working I would not change them! I think you expecting too much just from a different driver. A possible reason for overheating can be a too high setting on the current limiting. What mainboard Version do you have? Are the drivers soldered on the board or can they be removed?

But in both case the current limiting is set by a fixed voltage divider - would be very unlikely that this has changed! But would be good to double check and measure the reference voltage - I can send you a picture where to place the voltage probe. Do you have a voltage meter?

Problems with those wires certainly wouldn't explain y axis shifts, would it?  I get both of them intermittently, especially if I try to print over 35mm print speed, usually about 3 hour into printing.   

As I feel like I have ruled out everything else, I am convinced that the stepper motors themselves overheat, and just don't react to their signals.  I think new stepper drivers would fix this.

If anyone else has suggestions that explain x AND y shifts, I remain open for ideas.