Swarf Mostly –
Is there no tenon on your tool-post to align it with the T-slot?
Mine does have that. It would be worth fitting one, or even using two dowels. Much better than plastic mesh, as that could compress and put your height setting out, or possibly even act as a bearing washer, anti-slip or not, and help the post slip round.
Yes – in holding anything by T-slots the table flanges must always be compressed evenly between the T-bolt heads / T-nuts and the attachment itself.
A T-nut stud or screw must never ground on the bottom of the slot., and this is often avoided by a staked thread in the nut.
I have a set of those Myford T-fasteners too, and no, I don't think them a very good design either, for the reason you give. They certainly need careful use. Designed more for production than function, methinks.
I made a vice for the vertical slide of my little EW lathe, and that uses a T-bar rather than single nuts under the fixed-jaw end, with screws in counterbores but again with care that they cannot bear on the floor of the slot. The vertical slide itself is nominally held to the slotted cross-slide by a single Tee-bolt (not good) so I made two L-shaped "bench hooks" from steel bar, each held by 2 T-bolts in the adjacent slots, to secure against rotation.
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(Incidentally, digressing a little, I learnt from this forum that the common T-slot fastener sets sold by many of our suppliers have 3/8" UNC threads. With that information, I augmented the set by buying some shorter, matching bolts, plus nuts and washers, so I can secure things like vices through their slots – sometimes work-pieces through suitable holes existing in them – without galumphing great lumps of steel in everyone's way.)