You could make yourself an adapter to firmly attach to your pin mount on the Cat. What ever you do, you don't want to create two inline moveable points.It hard for me to explain but...... having a flex mount at the cat and at the trailer ball mount would be two swivel points. BUT, if you had only one solid attachment point you could make that attachment point a couple like a U joint in a driveline. Explanation..... When they used to use pull behind wheel or track logging arches behind tracked dozers, the connection point was usually a pin mount on the Cat. On the arch tongue was a pin point that was attached to a U joint like assembly that as attached to the arch. This allowed for rough terrain use so the attachment, meaning the arch could go up and down side to side and not but the set up in a bind, or bend the rat.... out of the tongue assembly.
Also, you might consider putting some kind of extension to lengthen the distance in the tongue length. When you get in some spots and start to back up you will see that having the longer tongue is easier to manipulate and lessens your chance of contact between the Cat and the trailer when turning.
On the trailer hitch - It might not be practical or necessary for your setup and terrain but my going here is pretty rough and would prefer a pintle hitch if I trailered with my dozer. Would take some fab work though.
When I was shopping for mine, I don't think I saw one on a lot that wasn't a ball hitch aside from the gooseneck models. Switching from a ball hitch to a pintle ring isn't a big deal...just a couple of bolts really. Mine is a 16' long 14K dump trailer and it uses a standard 2 5/8" ball hitch. I sometimes hook mine up to the draw bar on my Massey and it works out perfectly.
My opinion is use a pintle if you plan to keep it behind the dozer and use it often. Either would work, but sometimes we tend to push the limits more when there is a machine more capable to move the trailer and the pintle keeps it secured to the dozer as long as the pin stays.