Mountain Laurel Designs Duo-Mid came to mind
Go here and scroll to the options and you'll see a perimeter bug net for $45.
My duo-mid has it...it extends down 10 inches from tarp to ground and allows airflow coming up and under and into and then out the vent yet keeps the bugs out.
I think TallPaul was thinking the same thing.
No reason why this could not work with a hammock tarp especially if the tarp has doors BUT most tarpers hang their tarps higher than 10 inches, at least the tarpers I've watched set up---then you get into increasing amounts of netting and bulk as the OP stated, which equals more weight.
Last 2 seasons I've been good hosing my house and most other kit with permethryn designed for gear to create a no-fly zone for critters.....but I've not used a tarp for a while either :)