Hi Neal,
The two main issues with using 1 mil or any tape thinner than the 1.5mil standard is stretching and print through. If your machine's well adjusted as you say, the stretching shouldn't be a problem. A good precaution with any tape is to jog to fast forward before stop when rewinding. That allows the motors (which tend to be more consistent when it comes to torque applied to the tape) to slow the tape down before applying the brakes.
Also, because 1 mil tape stretches more easily, proper storage practices should be strictly adhered to. Always leave them in a played condition. The layers of tape on a reel have a force that "pulls" it toward the reel hub. When the layers of tape aren't laying in line with the layers below, the side that sticks out will become "cupped" and won't lay across the heads flat anymore. This causes "spacing loss" which is what we hear when a spec of dust gets between the tape and the head (a drop out).
When it comes to print through, some things can be done to minimize that issue also. The main thing that can be done is to record your tapes at a lower level. The smaller the magnetic imprint there is on each layer of tape, the less likely it is to migrate to the adjacent layers. (actually, the smaller and less powerful the magnetic field is but you get the idea). Now, don't get me wrong. Don't go crazy and record 10 dB down. Just be conservative in your recording levels.
Another important thing to do is to "exercise" your tapes a bit immediately after recording to it and a couple of times in the next day or two. All you need to do is rewind and fast forward a couple of times, then play it. That "exercise" moves what spot on the tape is on top of another spot on the tape.