Coolant system and heater core, suspect the heater core was gummed up with the liquid gasket?

I recently bought the truck listed above. The truck had previously had a blown head gasket that someone tried to fix with that liquid gasket junk. The person I bought the truck from had repaired the heads and put in new head gaskets and said he had done a coolant flush but there was no heat in the truck, and it needed the heater core flushed. He suspected the heater core was gummed up with the liquid gasket.

I flushed the heater core the other day. I attached a clear hose to the outlet pipe of the heater core and fed it into a large jug so I could see what was coming out of the heater core, then used a garden hose to force water through the inlet pipe. I flushed it until the water ran clear. Got lots of junk out of it. Old coolant and gummy junk.

I then decided to do a complete coolant flush as well. Sure, the previous owner had already done one, but if the heater core wasn't flushed I figured it would recontamination the whole system in the few days I had been driving the truck already.

I bought a bottle of coolant system cleaner and followed the instructions. I drained the coolant from the radiator, pulled the overflow tank and dumped it, and drained most of the coolant from the engine (I only opened the passenger side drain on the block as I couldn't see the drain on the driver's side). I replaced all drain plugs and the overflow tank, dumped the cleaner in the radiator and filled the radiator and overflow tank with water. I then ran the engine with the radiator cap off.

At this point, I'm pretty sure the coolant level in the radiator is supposed to drop as the water pump draws fluid from the radiator and circulates it through the system. However, the fluid level in the radiator never dropped. I ran the engine until the temperature gauge started to rise above the normal operating range. I let it cool and ran it again several more times and tried squeezing the top coolant line from the radiator, but the fluid level still didn't drop. I didn't seem to even get any air bubbles out through the radiator.

I don't think there is a problem with the water pump as the cooling system worked fine before I drained it. I suspect maybe there is a lot of air in the system? I am considering trying to jack up the front of the truck and seeing if that will help dislodge the air pockets? That's what I ended up having to do with my 06' WRX, but I'm wondering if anyone has any other suggestions about some other possible reasons why coolant may not be circulating, or other suggestions on how to get any possible air out of the system.