I would probably up your grain bill by about 35% plus get additional grain to add into the mash prior to taking second runnings
So 10.9kg pale, 1.1kg caraamber, and keep the chocolate malt at 80g.
Then mash maybe with a little extra water than what you normally would and just take first first runnings. Dilute that for the first brew and start to get that to a boil.
Do a batch sparge for the grain and add an additional 1.6kg pale and 1kg caraamber. Since the target for the second runnings is higher, it'll need more sugars. Let that mash while you get the first runnings to a boil and I think you'll be close to both targets. I would run off the second runnings then fly sparge the mash to get as much sugar as you can out.
Maybe keep some DME on hand if you miss a target, or just let it ride.