Securing Dock Lines on TI

I trailer my TI and launch from boat ramps. I have two 20 feet dock lines tied to bow and stern that I use to dock. When under way, I tie the bow line to the front crossbar using a round turn and two half hitches on a bight and larkshead the excess. I do the same for the rear on the rear aka. Tying off this way ensures that the lines don't loosen and end up in the water but I'm looking for something that is quicker to secure and release. Any suggestions appreciated.

Google "Rope Tidy Bag". Something like this hanging on the crossbar that you can just stuff the rope into then just tie a single knot to tie it off. If I was making one I would size it appropriately for the amount of rope and make the opening gather with a piece of elastic in the seam of the opening. Install a couple of grommets to hang it from. You could even install a cleat without fairlead to tension the rope near the bag. The nice thing about stuffing the rope in the bag is it doesn't tangle.
Chris