OK, I tracked down the problem, a VERY funny one 
Say I want to rotate something by arcsin(0.55), about 33.367. Enter that value in manual rotation field, verify the resulting rotation with selection info - perfect!
Now for more precision (???) calculate a more precise arcsin value using Windows calculator, you get a whooping 33 digits value (33.367012969231750012250966510535), copy/paste that in manual rotation value field... and... arghhl, when you verify rotation value in selection info, you get 35.07450 degrees! So it turns out that manual rotation doesn't like getting too many decimals!
Now just for the fun, enter an intermediate precision value (33.36701296923175001225096). Here the rotation almost reaches 90° (86.51408°)!!!
Hilarious, isn't it?
And - Yipeee! I now have a perfect fit in my model (current state attached)
Say I want to rotate something by arcsin(0.55), about 33.367. Enter that value in manual rotation field, verify the resulting rotation with selection info - perfect!
Now for more precision (???) calculate a more precise arcsin value using Windows calculator, you get a whooping 33 digits value (33.367012969231750012250966510535), copy/paste that in manual rotation value field... and... arghhl, when you verify rotation value in selection info, you get 35.07450 degrees! So it turns out that manual rotation doesn't like getting too many decimals!
Now just for the fun, enter an intermediate precision value (33.36701296923175001225096). Here the rotation almost reaches 90° (86.51408°)!!!
Hilarious, isn't it?
And - Yipeee! I now have a perfect fit in my model (current state attached)