My 2 cents... You shouldn't hear any whining (higher pitch) from the LCA's even with the firmer bushings. Since your stating the noise is middle, not on the outsides where you the LCA's connect, you may want to take a look at the carrier bearing and right at the pumpkin.
When you changed the LCA's out you did change the angle of the drive shaft. It's possible when the LCA's were disconnected maybe the axle move out of place far enough to put the drive shaft out of alignment (be it ever so slightly).
(I know what I'm about to say may sound crazy and unsafe but it can be done safely without incident. <~~~ But if you kill yourself trying it, I hold no responsibility.)
I would jack up the car, support the axle and the body in the rear, block the front tires, start the car and run it through a few gears and see if you can pinpoint the noise. 2 people would be the only way I'd do it.
Again, not trying to give unsafe advice. I've done it in the past and I used 4 jack stands and 2 jacks. I did safety overkill and I didn't go crazy on speed.