Re: T-Track for hanging, sliding, door

I'd go with the garage door track and wheels route.
T-track has close tolerances, and you have icing to consider on top of the bugs and dirt already mentioned.
The track would be hidden anyway with the wheels mounted a few inches down the lattice, thus raising the lattice to cover the track. A strip of lattice mounted like a drapery valence might be considered, if needed.
Let us know how it comes out.