While our circumstances are nowhere near the same, I suggested 2x a week early on with my T because I wanted to get through all of my crap faster. He agreed. (Maybe not for the same reason as me, but he knows I am a long term case).

It doesn't sound like you are at risk of bondinding at this point. There is no harm in asking if they have openings.

I too am avoidant. I have been seeing my T now for just over 2 years and I can only look at him for 1-3 minutes per session. I will talk but my eyes are anywhere but on him.