Unfortunately, I cannot help you much with your question about the clearance to the snow flap, but wanted to offer a few additional suggestions regarding getting the 156 to fit properly on your machine. Two tricks that come to mind for taking up additional 'space' (track length) are to add a larger rear wheel, and larger diameter drivers. For example, if you're running the stock rear wheels (about 7" diameter) you could switch to an 8" or even 9" diameter rear wheel, which will take up slightly more track length due to the larger circumference of the wheel. You may be able to get away with using 8" wheels on the stock axle due to the tip-up of the rails at the back, but typically moving to a larger wheel will require an offset axle. In addition to using up more of the longer track, the larger wheels will also lower rolling resistance and free up a little more power, though it's not likely to be much.
You can pretty much apply the same concept to the drivers, in that the larger circumference of a 9- or 10-tooth driver will take up a little more of the extra track length, and lower rolling resistance. In my opinion, there is an additional benefit to changing to a larger driver size as well. The larger diameter will place the track slightly lower at the front which will decrease the approach angle/angle of attack where the track meets the snow, allowing the machine to move forward rather than trench in deep snow. This decrease in angle as a result of the larger drivers would be pretty minimal, but coupled with the skid setback would likely be a significant difference. There is ample room between the track and heat exchanger to move to a larger driver size (depending on track lug size) so clearance should be no problem. The only real drawback that I see is that the larger drivers would act as if you had geared up (lower numerically), so you would probably want to gear down to compensate for this change in order to keep performance the same or similar.
Obviously the cost of the swap will increase if you have to buy wheels, offset axle, drivers, gears and chain, etc. I'm not sure what kind of mileage these components have on your sled, but if it were me, I would look at it as 'preventative maintenance,' replacing them with the new parts necessary to make the swap.