It might accelerate quicker with lower gearing, but 1st and 2nd run out of puff super fast, it only starts to get decent speed in 3rd! The key to a quick 1/4mile is getting out of the hole as fast as you can. Which means a good take off and less gear changes at low speed.
 

From memory when i had my pinto/t9 5 speed combo i was a running a 3.9 diff. 1st was quiet short, but then 2nd was quiet long and usable. Would just get to 100kmh revving the tits off it. Was a bit wilder engine than your running by the sounds though..

I would try a 3.9 diff first (with the 5 speed) which will let you use the torque a bit more. Being a pinto around 130hp it won't have wild top end cams in it like mine did, but more nice torque so the slightly longer ratio will lend itself to this.
 
Weight of the box won't have much if anything to do with it.. 10L of fuel weighs the same as the difference of the 2 boxes.

For the sake of a couple of hours work, I can swap out the diff gears quite easily. I'll give the 3.54 a shot and if I don't like it the 3.77's there to go back in
 

Quick update.
3.54 is in with the 5 speed.
1st gear is still too short! I think the best set up would be 3.77 with 2.98 1st gear.
3.54 still good and makes the most of the torque especially with my 38DG*S.
You just really have to watch what gear you're in at certain revs. 3.54 has made the motor hungry for redline, which you need to hit anyway for when the revs drop after gear changes. The best thing about it is when you back off, the car doesn't want to come to a halt like it did with 4.125! 
Cheers
 

Type 9's are renowned for having a short first and big jump to second, this is probably where you are loosing time in accelaration, im a pomme and have built kitcars and always played with cars with these boxes in. When I was a teen in uk cossie replica's were the thing to have but the gearbox still drove you mad when you wanted to go quick. A lot of friends played with various diffs etc, which improved (or masked) the problem. Before I left uk a friend changed the first/ second cluster from burtons if I recall, it really transformed the car, then he played with diffs, wheel size etc and made it into a real flying machine!