As has been stated, a Barker, which I have, allows you to turn the head 90 degrees. I had a Trailer Star which did not allow this. I would not attempt to drill an additional hole in your hitch draw bar. This would decrease the length inserted into your receiver resulting in more leverage exerted on it, possibly exceeding the design strength. Selling your jack, if it does not rotate, then buying one that does might be your best bet.
2015 GMC Sierra 1500
2013 Heartland North Trail 28BRS