The pros of stocking those bluegills now are:
1) You introduce a necessary species...based on your assumption there are no bluegills in the lake. If that assumption is correct, you'll make a good decision.
2) That 2-5" size range is deceiving...if they are mostly 4"-5", you've hit a home run.
The cons of stocking them now are:
1) If your ten bass actually did have a late summer spawn, and most of those bluegills are 2", survival rates are likely to be low.
2) The price of $.30 each is market price for 2-3" fish and you can get that price during spring, too.
3) Sounds like its more about the hatchery needing to make a sale than helping solve a fisheries problem.
4) This is probably the most important point. Stocking bluegill now gives you no advantage over stocking them in March. They won't grow, and they won't reproduce (unless you get a few back-to-back bluebird 80 degree days in February).
I still stick with the advice about doing the electrofishing survey and then make a plan. Stocking will be part of that plan.
If this were a new lake, with zero fish in it, I'd say go ahead and do it. But, that's not the case. You don't know what you don't know and that's what the electrofishing survey will help. You'll know more after that.
To reinforce that point, are there chain pickerel there? Where did the green sunfish come from? What about bowfin? With the species you have found, using the methods you've had, your samples are biased. Electrofishing mitigates that bias.
Do your habitat plan, electrofish the lake and then make decisions.
Speaking of habitat, what you designed and show in the photos is great transition structure. I like it a lot.
