This could be a compound problem. The wheel may have excessive roadforce and your diff could be on it's way out.
If you want to chase the diff:
For testing purposes, buy the LM stuff and add half of a tube. It doesn't really matter what brand. You can even get some GM friction modifier. Getting OE fluid is not cheap, however the tube is like $15. Mix it up a bit from some circular driving and go on a short drive. I doubt it's going to solve your problem considering you are driving in a straight line while the groaning is happening. Getting OE fluid is $150 and I can almost guarantee you it will not fix it. Diff bearings could also be failing. When you pop the fill plug off, stick a magnet down in there and see how much metal sticks to it. I hate to be the bearer of bad news but you may have something failing in your diff.
One last thing to consider is worn suspension under the downforce. Check for any scraping or leaking struts. This is a simple check and is highly unlikely but I have seen struts fail at 5k miles causing an oscillation at higher speeds. This would explain the changing of load and body roll. I'm still thinking you have bad tires and a bad diff though. I am not a fan of throwing parts at cars. That's not a diagnosis, that's a waste of your money.
If you want to chase the diff:
For testing purposes, buy the LM stuff and add half of a tube. It doesn't really matter what brand. You can even get some GM friction modifier. Getting OE fluid is not cheap, however the tube is like $15. Mix it up a bit from some circular driving and go on a short drive. I doubt it's going to solve your problem considering you are driving in a straight line while the groaning is happening. Getting OE fluid is $150 and I can almost guarantee you it will not fix it. Diff bearings could also be failing. When you pop the fill plug off, stick a magnet down in there and see how much metal sticks to it. I hate to be the bearer of bad news but you may have something failing in your diff.
One last thing to consider is worn suspension under the downforce. Check for any scraping or leaking struts. This is a simple check and is highly unlikely but I have seen struts fail at 5k miles causing an oscillation at higher speeds. This would explain the changing of load and body roll. I'm still thinking you have bad tires and a bad diff though. I am not a fan of throwing parts at cars. That's not a diagnosis, that's a waste of your money.
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