Unfortunately, it would actually be rather simple to fit Petry under the cap this year.
The scenario that makes the most sense is Khudobin gets traded to Montreal as part of the deal with the plan that the Habs are simply going to buy him out. Dallas may or may not retain in the separate Klingberg deal, which since we're talking about a hypothetical that Nill is knowingly threading the needle and not selling Pavelski/Rads/etc. let's say he doesn't and a 3rd team eats half his salary. Dallas now has $7,583,333 in salary going out. Say they retain ... that's $5.458,333. Dallas' extra forward right now going back to the AHL covers the rest.
The even easier solution ... teams have guys eligible for LTIR that aren't even using it right now. Kesler could be acquired for future considerations and make Dallas' cap issues disappear.
Unfortunately, it's rare that there's not an easy workaround. In this case, there are two very plausible workarounds. I still think there's a shot everything is sorted in a few weeks after the road schedule starts. It's possible that doesn't happen, but I also don't think there's strong evidence the team is about to do a 180 either.