the problem is that if you have to do an emergency brake i would think it would break either the straps/connections or the bike, the anchor points are at the lower portion of the bike, top heavy and kinetic energy would take over. its doable over a short run but I wouldn't try it over such a long distance.
I doubt braking forces will be an issue. Few street vehicles can brake at even 1G. Let's assume the LT weighs 850 lbs. I am not sure the height of the Cg of the LT, but I suspect the front fork attach point is at or above the Cg. The rear side case frame attach point may be a little below the Cg, which would increase the force a little.
If we assume a 1G braking acceleration, that will put ~850 lbs of lateral force on the strap attach points, which is ~425 at each end. Probably a little more at the front given the forward weight bias of an unladen LT. Let's say 500 lbs at the front and 450 at the rear assuming some amplification if the attach point is below the Cg.
If we assume a 30 degree angle between the straps and the bike vertical axis, the lateral force will be multiplied by two when vectored into the strap. So, the front strap needs to resist 1,000 lbs tension and the rear 900 lbs. Straps that will handle 2,000 lbs are readily available. I have no doubt the fork will handle that force, but I am less confident about the side case rack. I would probably try to find a second attach point for the rear.
I think the bigger issue is aerodynamic forces on the windshield and top case. However, assuming the trailer is behind a tall vehicle like a pickup or SUV, that is likely not an issue. I would probably remove both windshield and trunk since both can be done relatively easily. That would be extra peace of mind for a long trip.