Yes, I agree, but one aspect here stands out to me, The OP has a dead backup battery and has not yet IMO confirmed why it's dead, and there are a number of benign reasons it is, but if a short is involved, installing a battery with 10? times the capacity, even if the same voltage with no current limiting could be a recipe for disaster.

Reality check, that half the population is smarter then 50% of the people and it's a constantly contested fact.