Wondering about your mains charger. They usually supply more than enough current to do the job.
That said, have you considered surgery on your old ONE XL for a new battery? Not sure it's worth the hassle given that maps are no longer being made available for it, but it's an interesting DIY job.
You need a charger with a voltage of 5 volts and an output of at least 1.5 amps.
Most charging power supplies only have 1.0 ampere - that's too low.
the TomTom ONE 1st Edition Serial: G1xxx or G2xxx needs a higher current