So I haven't necessarily gotten to a point to where I can burp the system. Without the brakes, I am unable to get it somewhere to lift the front end or get it on an incline.
I did however take the radiator cap off, filled the radiator to the brim with coolant, and make sure that the overflow reservoir had coolant in it as well. With the cap off I started the engine, turned the heat on and went back and forth between watching the temp gauge and watching the coolant level.
While doing so the coolant seemed to steadily seep out of the top of the radiator. The level did drop down once but then came right back up and poured out of the top again. The temp never got past the halfway point on the gauge, and the air coming from the heater never really got warm. I let it run like this for probably 10-15 minutes.
While I had it running I reinstalled the radiator cap, then watched the temp steadily rise. The radiator fans didn't kick on until the temp gauge was at approximately 3/4 but it steadily got warmer. Once the the gauge was between 3/4 and red, the fans kicked into high but again, it kept climbing, and I finally shut it down.
Last thing I noticed was while checking the coolant lines coming from and going to the radiator after I shut it down the line coming into the bottom was definitely hot to the touch but the top line coming out of the radiator wasn't hot at all.