Welcome to the PB forum and a good first post. With that size pond you can manage it as you noted using Sunil and Theo's suggestions. With only 4 LMB do you know if there were both male and female in the 4? Same question for the BG. If you use the "more LMB" method using 10-12 in. fish you will need to take some out in about a year. It would be good to add some LMB of all sizes in the add-on group so you will have different year classes. They will also feed on the various sizes of GSF more efficiently than just a bunch of 12in. LMB. Your June 3 LMB had probably spawned by then given your location. Don't count on their this years offspring. If you could get about 20 4-6in LMB and a couple of 16in. ones to add this fall it would be good. I would, over the rest of this year add about 20 more adult BG some of each sex. Here is a link (see pgs 10-12) about pond balance and what you should see and look for. Seining ,trapping and fishing of the pond will give you info on what is happening and a way to help the process of GSF removal. Let us know how it goes.

http://msucares.com/pubs/publications/p1428.pdf