Toto Eco Drake flush handle questions

Hey all,
I recently installed an Eco Drake in our master bath and wanted to put a flush handle that matched the other trim items in the room. I bought Moen handle that matched our shower trim but upon installing it realized it doesn't fit in a standard way and requires to to pull up to flush vs. pushing down:



anyone have any thoughts on how I could get around this? In another bathroom we have the Promenade which doesn't have a problem because the green valve tower sits low enough in the tank that you can orient the handle in the proper way.

Has anyone been able to use non-Toto handles on the Drake?

The Drake has an angled tank, sort of like the Kohler Wellworth tanks.
The brass rod on the Drake tank lever has bends that fit around the fill valve.

The trip lever pictured has a square pin and set screw, what happens if you rotate the lever 90 degrees?