It's not so much the diameter of the tire being the problem rather than the ongoing difference in traction/resistance causing undue stress on the differential AFAIK. By diameter I mean tiny differences on tires that are the same size. Obviously running a 15" tire along with 16" tires on an AWD (or FWD/RWD on the drive wheels) is a bad idea any time.
The diameter is actually a key part of it. The AWD systems want everything to be turning at the same rate, and they will propel the tires to keep all four of them turning at the same rate. Now, if one of them slips, it sees that wheel turning faster than the other three, and will react (cut power to that wheel, add power to the others, et cetera). So it's not so much the traction/resistance, it is how fast the wheel is spinning (or not spinning) in relation to the other wheels, and during normal cruising (i.e. not slipping), the diameter is the only real effect on that.
If the diameter of one wheel is larger than the others, it will travel further with each rotation, yet the drivetrain only supplies it with a certain rotation speed - something has to give. So the drivetrain thinks that tire is constantly slipping, and thus is constantly making adjustments, and it isn't happy with doing that.
Most AWD manufacturers have rolling diameter tolerances, with 2-3% being very common. So if you're driving on a 225/50R17 tire (it's a pretty common size) with 8/32 tread, you have a rolling diameter of 670mm, while 4/32 tread makes a rolling diameter of 664mm - that's about .5% difference. It's a pretty small value, I don't know exactly how sensitive Subaru is on that. A computer-controlled part-time AWD generally won't notice. So yeah, the major problem is differently sized wheels/tires, as you suggested, mixing 15 and 16 inch wheels.
I would actually think the OP could get away with a tire of the same size, similar wear level, and similar type. So a used all season tire of fairly average grip, in the same size, with about the same amount of tread left, might work. It should be measured unloaded compared to the tire it would be replacing, as some manufacturers do have variance. Example: I recently put snow tires on a car, two separate pairs of them, and found that one pair, despite being the same labeled size, was actually 1/2" taller. Fortunately, that was a FWD car, and it doesn't care.
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