Frost in ice chute, even after replacing flapper door

I have had a problem with ice buildup in the ice dispenser chute and on the undercarriage of the ice bin. I replaced the flapper door a couple of weeks ago but I am still having the problem. After replacing the flapper I held a flashlight up to it and looked down through the chute and could still see some light, although less than before replacing. I tried stuffing a rag on the outside of the flapper door (held in place in the clear chute/guide) to try to close off any remaining gap and provide insulation, but I almost think that made it worse.

Is there something else that could be causing this?

The frost buildup every few days gets so thick that it catches the ice when dispensing and causes jams.

Thanks in advance for your help!

Kathy