Jeff....
This an excellent idea and you would get good penetration and bonding with a mesh!!!
But..... I will have to say i wouldn't use epoxy. I DO realise it is an excellent glue, i really do, but our door panels (like any form of plastic) are not porous in any way and i still maintain a good polyurethane sealant ( as an adhesive) would be superior in this application, after a damn good scratch/abrade of the surfaces to be be bonded. By it's very nature it will cure with a very slight flexibility to it whereas epoxy dries hard and brittle
I have experience of both, plus loads of others in my work as a college lecturer in design and technology and my panel is still as good as the day i did the repair! The product i used was Sikkaflex 221 and this link will go a way to explaining!!
http://www.sikaindustry.com/tds-ipd-sf221-ind-us.pdf It is rather a long winded PDF file but basically apply,spread,and bring together the two layers.
Please believe me that a well roughed up surface and a good layer of this product or a very similar type will be spot on ( maybe lightly clamped whilst curing, also)...
I am an old git now, well... not
that old.... and have seen it all in my work over the years!! Keep me posred
Trev... :o)