How can I stop the gurgling in my heater core and get better heat?

What is your question?

After draining the radiator and flushing the heater core there is air trapped in the heater core that I can't get out. I don't think my 2.2L 4cyl has a Ac bleed valve. I tried jacking up the front and running the car with a no spill funnel attached to the radiator for about 30 mins. Lots of bubbles came out, no doubt more were in there but I can't run it like that forever. The sloshing sound is still happening when accelerating from a stop. The heat is much warmer since flushing the core, but it could definitely be warmer. My driver side rear carpet seems slightly damp too. Checked the AC drain and it's in good condition and not clogged. Replaced the temperature sensor and thermostat. No over heating. No coolant loss. No white exhaust smoke. Can this be remedied or do I need to replace the core?

What makes this problem better or worse?

It’s better after the car has been running for a while

How long has your 2001 Toyota Camry had this problem?

A few weeks