The good news is... the odometer over-reports by a couple percent.
Thus, to avoid litigation, Honda extended the battery warranty to 157,500 miles.
( USA only )
So you have a little longer to try it out.
I have owned a used 2000 for 3 months.
The battery meter is an estimate only. It is not absolute, nor is it an exact science.
The computer will "recal" or recalibrate once in a while.
During daily use, the power bars should move very little.
Every so often they will go down really fast, and then they will slowly come back up. This is a recal process. On my 8 year old car with original battery and 80,000 miles, I get about 1 recal per tank.
I think the non OEM tires are what is causing your car to have a sluggish feel on the highway and on hills. This car with a 996 cc engine has zero power to "spare" pushing around larger or softer tires. Heck, I have to drive in 4th gear on the highway if I have a head-wind. Look out! when you have a tail-wind though... 80 MPG highway is very likely, but it works both ways of course.

-John