Can my lug and breaker insert be rotated 180 degrees
That right there is what a panel should look like. Note the empty void for a third service wire; that's for 3-phase which means it's industrial grade. The breakers are 3/4" wide; this would only fit 20 breakers if they were 1" tall.   It's very, very busy in there, but only because all the wires come in the top hole.  It's not anything to worry about.  They did you the disfavor of  runting off all the wires so they barely reach the breaker/bar, which frustrates moving anything around or adding AFCIs/GFCIs. But here's the thing: 

Ground bars do not need to be in the factory anointed locations

They can be placed anywhere in the panel. except the screws can't mount on a knockout (it can bridge across an unused knockout).  But you need to very carefully drill and tap the mounting holes yourself, -32 pitch or finer,  typically an 8-32 or 10-32 or 1/4-28 screw (whatever they provide in the kit).  The holes must be the right size, which means looking it up on the web and hitting a hardware store for the correct bit, probably a numbered bit like #27.  I would wrap the drill bit with masking tape so only the first 3/16" is exposed, so it can't nick a wire. 

If you strip out a hole, just move the bar over 1/4" and try again. 

Mind you, the -32 requirement is for electrical contact.  I wouldn't rely on it for electrical contact. I'd use a nice fat ground wire also,  going from the ground lug you're abandoning through your first bar, through your second, pop up a little for the clamp meter, and then onward to the neutral bar. 

As far as flipping the bus bar assembly

It looks to me like Cutler Hammer went to a fair amount of work specifically to make the bus bar assembly flippable.  But that appears to be so they could do it at the factory, because there's a problem. 

The cover won't line up.  You could contact Eaton and see if they can supply a cover for that; it's possible.