Fans PULL air much better than they push it ;)
If you have room in the ceiling above the grill, why not hook up a fan in there temporarily and see what happens?
Double stick tape the fan to the top of the grill, stick the wires out between the grill and the ceiling and hook to a 12v source.
Now here is the crux....
You have to run it for at least 20-30 mins to evaluate it. Initially it will seem like a MAJOR difference, pulling cool air out of the ducts faster.
...but...your A/C only has a certain cooling capacity. If you move more air through your ducts, there is a point where the A/C cannot effectively cool that volume of air.
The good news? If recirculating the air, you will be feeding cooler air into the A/C as you go, meaning the A/C performance can actually be better than simple...(too much detail and likely others are more knowledgeable about A/C performance curves than I am, so I'll stop there, LOL)
I think the rough and thin ducts in our campers can use all the help they can get for moving air. Should be a good result ;)