"Placing the rigid tank higher than the head isn't all that big a deal."
I'd be scared. The only thing preventing the sewage--or water--in the line from running back down into the bowl is the joker valve, and those always leak sooner or later. Unless you pump enough water to ensure there's just "clean" water in that line, it is coming back into the bowl. And if you pump that much water--there goes the extra capacity.
Even with a siphon break in the line...I'm not sure there's anything to gain because of the excess water pumping through to go "uphill" and flush the line to the tank.
Can you perhaps raise the head, and install a holding tank under it? Gut the head, and install more holding tank across the head floor?
Raritan and a couple of the other tank makers have huge catalogs of standard sizes--that the chandleries just don't show or stock.