Hey jrbsr I fish almost exclusively with braided line and sometimes you just have to loose some lures. I am primarily a shore fisherman as well and have developed a few tricks to get my lures back.

If you make a bad cast into a tree or some other shrub just let your lure go over the branch and let it fall. Then reel it back to you as fast as possible so you whip it past the branch. If you try to get it out slowly you give the hooks too much of a chance to get stuck.

Underwater hangups from the shore are another story. Once you first notice that you are hung up don't pull harder because the hooks will only get stuck more. Wiggle your rod tip a little to see if you can't shake it loose. If not I will let out a little bit of line. I will take a towel and wrap it around my hand and then wrap the line around that so I won't cut myself. Then pull straight back on the line until either you pull up whatever you were hung up on or your knot breaks. I have pulled up quite a few logs with this method. Sometimes you just have to just accept the fact that you are going to loose some lures though. I find that I loose far fewer lures with braided line than I ever did using mono.