Cheap drip edge for an old garage

I have been replacing the rotten fascia board and guttering at the back of my concrete sectional garage. It has a corrugated asbestos concerete roof that slopes to the back.

The roof overhang at the back is not large, and the replacement timber I have used is slightly thicker than before. After fitting the guttering I found gaps between the overhang and the gutter, where water could flow down the fascia.

Could this be alleviated by fixing some sort of drip edge? It seems that roofing felt has been used previously.
As it is just an old garage, I am looking for a cheap fix for this --- maybe I could make something up from good old useful plastic?

I might do a rejig of the guttering, to minimise potential drips as far as I can. Then use some flashing tape as a drip edge.

Felt support trays (if you can slide them under the asbestos without breaking anything).