The squares in the back are those iron pontiled hostetters from a couple weeks back. I haven't figured out what i want to do with them yet.
As for the reconstructions we usually split them up among the group of us that dug the pit. I have several hundred early ceramic pieces now they make for a great ceramic collection without paying the prices this stuff goes for perfect. I also have a friend I trade broken things to in exchange for ceramic restoration work. The broken ceramics can often be better then the bottles of similar age. I have most of mine displayed in my office but its about full so I'm planning to start filling another room soon.
When I first started digging I used to put all the broken stuff back in the pit. Then I started digging with a few oldtimers that saved everything. It wasn't until we dug an 1820s pit that had a London mustard a black glass cylinder and a 3 piece break historical transfer saucer were the only finds and I ended up with 3rd pick and took the broken saucer because it was all that was left a couple days later I washed the broken saucer and saw it had great American eagles with shields on them transferred onto the saucer. I ended up researching the mark on the back and found that the saucer dated from 1818 to 1826 and after that I was hooked on early ceramics.