While I'm waiting for the new rocker arm pivots to come in (early next week), I went ahead and dived into the timing chain (403 V8). I'm able to line up the gears to be dot to dot, but then I take off the top gear to chain both of them together, and when I put it back on I've found consistently the cam has moved on its own so it's no longer lined up. Is there some kind of tool or technique to this? The manual doesn't mention anything but I feel like I'm missing something.

 

You have all the rockers loose, right? This job is nearly impossible with any rockers tightened down because the lifters will be trying to turn the cam.
Otherwise, the cam will drift a little. Just use a screwdriver or something to line it back up. It should turn freely.

 

The force of the valve springs pushing on the lifters often causes the cam to move if the lifter is on the opening or closing ramp of the lobe. Obviously loosening the rockers eliminates this, but I've often just been able to move the cam by hand to line it back up.

 

It didn't in my case, but I wised up and instead of messing around with the cam some more I instead turned the crank which moves freely but doesn't walk by a proportionate amount in the same direction, and then double checking with the chain on to make sure it would be dot to dot. Worked pretty well. If I had to do it again I'd use a degree wheel and some fancy proportion math to get the exact amount to turn the crank to get it the first time.

 

Just turn until the dots line back up when the chain is installed. If they line up, then you're good (for a given value of "good"). Being off by an entire tooth is pretty obvious when checking.
Degreeing is useful to check to see if the timing chain is actually marked correctly. It's common for the keyway in the crank sprocket and the pin hole in the cam sprocket being off, which means the cam to crank relation isn't correct. A degree wheel lets you directly check that relationship and, if the sprockets have multiple keyways or other adjustments, change the relationship to get the cam where you want it.
Or line up the dots and send it.