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Yes the TL-71 wobble a bit more than TL-75s on my 80-series meters, but not so on the older 70-series. Primary reason is that the jack inside diameter is over 1mm larger on the 80s, so the shroud does not fit snugly at all. Also, the TL-75 plug has a 4mm solid post that is split to make it springy, whereas the TL-71 plug uses a lantern-style spring on a thinner post.
The TL-71 plug shrouds have a small band up near the strain relief that is a bit wider than the rest of the shroud. If you trim about 2mm off of the shrouds, they will sink farther into the jacks. This band will then fit into the jack perfectly, which will make the whole affair quite snug.