If it's only an issue when the motors are enabled it's almost definitely related to either noise or a ground loop. I had a look at the datasheet for the chip used in these encoders (MT6816) and they use push-pull outputs. They are however quite weak at only 2mA so with the fairly long wire runs in a noisy environment I could see them struggling to overpower noise, inductance, and capacitance. Especially with the relatively sensitive inputs on the teensy. Therefore one thing worth trying and even mentioned in the Teensy Encoder library is to add external pull-up resistors. If you have some resistors available I'd say it's definitely worth giving a try. I'd try adding pull-up resistors for both of the J6 encoder pins (24 and 25 on the teensy) first as it should, in theory, be the noisiest. If possible start at something like 100K then 10K and finally 1K. Of course, if one of the higher resistance values solves the issue there's no sense in going lower as it would just stress the onboard voltage regulator unnecessarily. Just to be clear add these on the teensy side, not by the encoders on the robot. Other than this I don't have many simple ideas left. A low pass filter with a capacitor might help but that starts becoming a lot of extra wiring if you don't want to spin up a custom board. I'd of course be happy to send you the files for the differential driver boards I made if you ever feel like sending in the cavalry but they take a bit off setup too. (Not at all difficult mind you, just time consuming)

Does it blink with one of these patterns?

I struggled with this issue for forever. The best advice I can give is to make sure that your cable shield is properly terminated and that your wires are as short as practical, a complete rats nest in the robot base will exacerbate the issue. With all that said while I managed to make the issue less pronounced with these methods I never managed to make it fully go away. I ended up going all in and designed some custom PCBs to utilize the differential output of the encoders. This works perfectly but it was a decent amount of extra work.

Unfortunately I don't think this is possible for two reasons. The torque of the steppers with the specified drivers can't be controlled in software, it's set by the current setting with the physical dip switches on the drivers. Secondly almost any amount of holding torque would make it very difficult to move the axes accurately espcially the J2 axis with it's 50:1 gearbox. To implement this properly one would have to install strain gauges or some other kind of force sensor on each axis. Which is definitely doable but not without modifying the robot. Feel free to correct me if I'm wrong though, would certainly be a useful feature. :) The 3-5 could sort of be done with the E-stop though with some mild software trickery.

I'd go out on a limb and say it isn't necessary if it's a snug fit, the friction between a plastic on plastic or plastic on metal interface is much higher so if it's a snug fit it shouldn't really move that much. I'd worry that any dissassembly with would become destructive on a plastic AR4 with retaining compound. If it's a loose fit however I'd consider adding something like a bit of carbon fiber grip paste.

I've been doing this by just starting the program once from the PC and then having it wait for an input on the arduino (though I use a pi pico) that I have wired a button to. So it's one work around to the problem.

I can't speak for local places but RS components and McMaster both have 1inch tubing and work well in Europe, they're of course not the cheapest options though McMaster especially.

Thank you!

While an airbrush compressor could probably run the gripper if that was the only thing it was doing, you have to keep in mind that you'd never be able to get the maximum amount of grip strength since those compressors are typically rated at (a somewhat generous) >4 bar. The cheap ones also don't have an air tank so your actuation times might be quite slow compared to one with a tank.