Went to a Marshall's at lunchtime and may have found a suitable candidate. They are DKNY crew neck t shirts. They are very soft and thin. Haven't washed one so I'm not sure how they'll hold up. Also, the tail is long, which helps is good for them not riding up your back. Really happy so far. I was able to find an open package, which was marked down to $7 for 3 shirts. The regular price @ marshalls is $14.99. MSRP is $29.50. I think these are the ones:
Check the reviews as others agree that these are very thin.
I'll still try to get one of those micro fabrics @ macy's just for comparison's sake. Hope this helps someone...