The magnitude of TIM is highly dependent on the open loop gain (everything else being equal) up to point where output transistors go to momentary saturation and stay there for a moment (having charge trapped at the junction).
No, I think you're getting a couple of concepts confused.
Saturation of the output transistors happens at clipping or at reverse bias, the latter of which being a point where the charge carriers are accelerated maximally away from the transistor junction. Whether or not this happens is indeed a function of output stage slewing, but is completely an open-loop phenomonon and occurs independently of loop gain. The amplifier need not have feedback (actually it doesn't need small-signals stages at all!) for it to occur. If for some reason the designer wishes to never reverse-bias the output transistors, this is easily acheived by making minor changes in the driver connections - and the result is a slightly slower output stage.
The concept of slew rate limiting that Otala discusses in his seminal paper on TIM is related to the charging and discharging of the capacitor(s) used to set the small-signal bandwidth of the input and voltage-amp stages, and thus the open-loop response corner frequency. Since these small-signal stages are always biased Class A, their slewing performance (and ultimately that of the whole amplifier) is dependent on the quescient current flowing through them (as used to charge/discharge the capacitors), not the open-loop gain (which BTW I'm assuming means the o/l gain below the corner frequency). Otala advocated the use of capacitors in different places (lag compensation), which basically simply changes which stage in the amplifier is responsible for their charge/discharge current. Both Otala's method and the conventional approach have their pluses and minuses . . . and both approaches can be much less drastic with modern semiconductors than the ones available when he wrote the paper.
My point is that TIM can be understood, analyzed, and avoided - and we don't need to go down the "is feedback good or bad?" road to do it. The latter is of course an unsolveable debate at this time (so let's not go there). The biggest point to me about THD, IMD, and TIM is not so much is not what the numbers themselves are -- but what's causing it, and what the best ways are to fix the problems.