What you described is almost like mine. So when I slow down to around 10mph to make a turn, and later step on the gas pedal gently, it kind of revs up for a few seconds (2-3 seconds???) and then it “catches up” - not sure if that makes any sense. But it doesn’t do that all the time, not even half the time. My mech calls it a slip.

RE: the mounts: front mount is located directly in the front center-ish area behind the radiator at the bottom. The rear mount I believe is located also at the bottom but toward the back of the engine. I think my mech said it mounts both engine and the tranny. The transmission mount is on the drivers side - I think mech said it’s behind the drivers wheel well plastic shield.

 

Yes, mine happens kind of in the same situation as you described. I don't think mine is a slip, as i think it's not sure where it should be, or in which gear. As i said. If I'm accelerating from a dead stop, it shifts through the gears perfectly. I think also, i will do a tranny drain and fill and use toyota products (not sure what was put in).
as for the mounts, i've seen the big one at front bottom, bottom drivers side, the one next to oil filler cap. But not sure what else there is.
so did changing the mounts get rid of your Slippage?

 

I still have the slipping once in a while. And like you, when I’m at a complete stop, it accelerates fine. I might just do a drain and fill for now.

 

My 2008 RX 4WD with 78k miles has both of these issues, exactly as described.

The hum, or droning sound, seems to pulse a little. It's especially noticeable when the engine is under a modest load, as in accelerating gently up a hill. It seems to do it more when temperatures are about 70F than otherwise. No impacts on economy or driveability that I can see.

The transmission slip seems to be only noticeable when I go over a speed bump. There's one near my house that I drive regularly and if I touch the gas pedal immediately after the bump it takes a second for the transmission to catch up. If I wait a couple of seconds after the up-and-down, it behaves normally.

Thanks to those who have posted some ideas, especially for the hum. There's some stuff I hadn't thought about there, like engine mounts.