I got in contact with the immigration office again.
I was informed that there is nothing keeping me from travelling before my permanent residency goes through, it's just that there cannot be a guarantee that I'll be allowed back into the country. Any trip I make is made with the understanding that I may not be allowed back in, and this will be true even for a few months after I receive my permanent residency.
Now, obviously I have some obligations I'm not going to miss, so I'm going to have to take that chance anyway.
I was informed that many people do travel in my situation, it's just with the understanding that there is always the possibility of consequences.
I asked for advice as to what I could do to minimize my chances of not being allowed back in.
"Were would you be going?"
"Well, this is going to sound weird when I say it, but when you go to the US don't rob any banks."
So that's the advice I got.
Looks like I've got some plans to make.