Ideally I was looking at how to hide the fields but that doesn't work - it just brings up incomplete field errors even after adding hidden tags like in the easy checkout mod - which didn't work for me at all.

I'll have a look at register.php ;)

Another quick question...

customer/main/customer_details.tpl

Is this only used to display the info on the last checkout page or is it also used for the order email or anything?

In other words is it safe to totally mod this up without losing functionality anywhere else within the store?

Yep, just the last page of checkout...edit at will :)