I thought shake at 55-60 on the E34 was built in by BMW as a standard feature which turns itself on at 100k!
There are any theories surrounding E34 shimmy, in my experience the front suspension of these always goes off at around 100k and every garage you visit has a different bit they replace to 'fix' the problem.
I would suggest that although your steering wheel may not appear to be affected, the fact that if you reduce the tyre pressure would indicate that it is suspension related. Got to a decent independent BMW specialist and get them to check the front end suspension out.
Don't know about US specs, here in the UK/Euroland we prefer things to be quite hard, whereas traditionally US don't. So BMW US might soften the suspension up for you guys, different setup etc. from UK, who knows!
Don't ride around on tyres at 22psi! Well, in the UK tyres are 31 front 36 rear - 22 would be mighty low - but as I said, may be diff. for US.