well you have some options..........

set the existing tank at max and add a tempering valve, that will
automatically mix hot and cold water to limit the maximum temperature
so no one gets scalded,

you can test this approach set tank as hot as it will go, wait till
the tank is hot burner off, then fill tub

if you can fill tub successfully your all set but add the tempering
valve so no one gets burned.

or add a large high capacity tankless as a preheater , tankless first.

the water must be heated anyway, so preheating costs little beyond the
upfront costs.

the tempering valve is the most affordable approach