Rather than modify your existing mesh tent, why not make a whole new base tent? You already are going to make the walls of the tent and handle the additional challenges of adding doors, windows, and whatever system you will choose to use to attach the poles to the body (pole clips, sleeves, or just webbing/grosgrain loops). The only additional step/cost would be making the floor. This way, you have a body for 3 season use, and a body for sandy conditions as well.
As far as materials go for a DIY, I haven't seen much lighter than 1.1oz uncoated nylon. Maybe someone else has seen a 15D or 20D out there, but 1.1 oz 30D is about the lightest I have seen.
Have you considered just fashioning a "skirt" of sorts to fit around the base of the tent? Something that would effectively raise the height of the floor to stop any windblown sand that gets in under the fly. It may only take and additional 6-12" of material, wouldn't be permanent, and would still maintain the integrity of the current tent.