A Triple 4 (.444) is a great ctg., even with the Marlin 38" twist rate. Mine did very well with 265gr. jacketed as well as 300gr. jacketed and cast.

However, please measure the rate of twist poprivit and see if it is in the realm of 18" to 24". If so, it will be even better for use with 300 or heavier bullets.

The H&R Handi rifle should easily make 2,200fps (same as Marlins) and perhaps up to 2,500fps with the 300gr. bullets depending on how the rifle handles pressures up to 50,00psi or a bit over. Considering that rifle, (if the EXACT SAME ACTION) is chambered in 60,000 to 65,000PSI rounds.