I still question using a sling load with antigrav. Seems it would be like picking yourself up by your own bootstraps IF there is a thrust/counter trust situation. Any thrust (inverse gravity) would project downward onto the very load being attempted to lift. Now if it negates gravity, that's another animal altogether, but then negation would just be a zero sum; no lift.
That depends entirely upon what it uses to thrust against, Vladika.
If it grabs the fabric of spacetime and pushes against that, then a load slung isn't being pushed against.
If it generates thrust only at the thruster-plate and the most dominant gravity source (as some have postulated over the years, and supported by the mechanics in TNE and T4 for "drop-off" of effect), then again, the slung load is meaningless - it's own gravity well is too faint to matter.
If it generates a direct downforce below it at, say, 45°, a small enough slung load would be an issue but not an impossible one.
Working an example...
MT Air/Raft, open topped
Mass, loaded 7.2 TmMass, unloaded 1.6 Tm8 Tons thrust (Tt)
assuming a trio of plates of about 2 square meters each...
at 0m, that's 1.333 Tt/m2 or about 13330 N/m2, or about 1.9 PSI.
We'll put the plates even on the bottom, and 0.25m from the ends for the fore and aft. That puts (on the 3m long) 0.25-1.25, 1.0-2.0, and 2.25-2.75m, all at CL±1 on the beam of ±1.5. (this looks to be good enough for matching the illo for now.)
Slinging 500kg of wood, at SG1, in a cylinder 0.6m diameter (a 2' diameter tree), we get a 1.75m length.
Slung horizontally, 1.75x0.6m=1.05m2 if it's slung flat underneath.
At 1m below, Assuming it's center slung, it's fully in the field of all three... and sucking up 1.05m2 of the total 3x4m of downforce each... or about 0.0875*2.666 Tt * 3plates = 0.7T. The effective mass for stress is
0.5T+0.7T= 1.2T on the cables, and only 7.3T lift.
Now, we rig it at 2m. It's still only 1.05m2, but each plate's hitting 5x6m, or 30m2... it absorbs only 0.035 * 8 = 0.28T, puts a cable load of 0.78T, and leaves 7.62 Tt... That slung load is easily lifted. (Oh, and it's pushing 0.36 PSI - mildly uncomfortable.)
At 3m below, it's now hiding within an area per plate of 7x8=56m2... 0.15Tt transferred to the load. It can now be rigged under even a "loaded" Air/Raft - because it's 0.65T cable load, and 7.85Tt still available.
Note that the math for helicopters works very similarly.
So, even if it has to be a beam "pushing" down, it can be done.
Now, assume that tree is 3x as long, and has 2 buddies. 4.5T of tree, and bound into a triangle, about 2x3x1.05=6.3m2. Yes, 5m trees. Too big to fit inside, now. At 3m, it's costing 0.9Tt, loading 5.4T on the cables, and leaving 7.1Tt - you can carry a full load of fuel, 4 guys, and some smaller trees in the bed, and still fly with this trio slung 3m beneath.
So, even then, it's logically slingable.