The braids with a skin, wrap less, Fusion??, but there are tips that do not have the bracket shoulder that will catch the line behind it, but expensive buggers they are. Also you can take your tip replacement glue, or candle wax and fill in that little gutter where the line usually catches on the standard tip frame.
Besides why is your line so slack that it can wrap the tip, grimming as I type this question? if it is happening during a casting motion get the weight moving before a round house or tip flip. I am plug casting a lot with braid, if I make sure the cast has no sideways arch the tip wrap, and plug wrap does not happen.
PS if you are trying braid for the first time be sure to get take a forcepts with a rounded nose for picking ultra small knots out. You will need them with cutting edges, to cut 20-30# braids, nail clippers are not going to work. I hang my forcepts on a lanyard around my neck, and get the heavy duty stainless ones from BPS. If you fish as often as I do, expect to have to replace the cutting edges once a year.
PS I like Spider Wire Ultracast, been fishing most brands for 12 years now.
I doubt if any roundness will keep braid from pulling into the reel. The real problem is the pressure you put on that spool. To pull a braid off a snag, point your rod tip at the snag and reel up the slack to the boats edge. Point your arm at the snag, put your forearm between the rod and the line and spirell the braid down you forearm twice and off you finger tips. Fell the line tension over your hand and fingers, now back up slowly. I have opened 5/0 Owners with 50# test braid doing this and have also towed the boat over to the snag if it would not give. And the reel spool work fine after doing this.