I did remove the channel cover but the lower sash didn't raise much more.

Like you mentioned, I may have to remove the lower sash completely to achieve a more open space for the fan I put in the window.

Did you remove both sides? I don't think think that there's anything else on that window that prevents the lower sash from traveling up until it stops against hardware. That said, its not much more than 1-1.5" of added travel even at that. Removal of the lower sash, ( practical and you have a safe area to store it) may be your best best bet for max airflow.

Yes I did remove both sides but I think the actual hardware in the channels limits how high the sash can go.

I'm no longer at home to send a picture to show. I'll have to try later today or tomorrow.

At some point, the balance clutch hits the balance tube as well.

Just tried a couple samples and they lower sash traveled all the way up until the hardware touched. It's possible that could vary based on the height though.

I squeezed another inch out of it by raising the balance hardware located in the side jambs.

Now it raises up to the top sash handle.

But I just came the the realization that I'll need to buy a new smaller (same BTU) window A/C.

My current A/C unit will not fit.

I would look at one of the floor units that then vents via hose out the window or side of the home.