You just need to get with the times and go lithium. Either get some 18650s and build a pack with some vruzend connectors or buy some factory built packs from a hybrid or electric road vehicle.
I paid $500 for a single LG Chem battery pack out of a Chrysler Pacific hybrid minivan. Its 16s1p 45ah, weighs 40lbs. Can do over 200amps continuous or 400amps peak. For your current draw you'd see very minimal voltage sag.
You would need a BMS and a charger as well.
---------- Post added at 04:16 PM ---------- Previous post was at 04:04 PM ----------
Oh yeah, FA what you proposed will help you, but only fractionally.
Your idea would increase the capacity of one of your 5 batteries. Let's say that capacity increase is enough to stop the voltage sag for THAT battery. The other 4 batteries will still have the same voltage sag so you'll theoretically reduce your voltage sag by 20%
1) my ElMoto (electric motorcycle) is powered by a 2kWh lithium battery pack (from a Chevy Volt)
2) building homemade lithium packs scare me
...too many variables (differing cell capacities, different resistances etc.)
IMO one would need a bunch of (really) closely matched cells
...& also, some good equipment, to verify them as such, to "safely" proceed
3) I really like your kart
...but, I build a lot of karts & find it kinda hard to justify $500.00 for just the battery pack
…& then/plus a BMS & charger
4) OK, makes sense
...adding (1) cell to a (5) cell battery pack would/may reduce sag by 1/5th