JIS drivers looks like Phillips but have a slightly differently-shaped tip that gets a better "bite" on the screw and allows you to get more torque on the screw before cam-out than a Phillips driver.

JIS originated in Asia in electronics manufacturing where Phillips cam-out is much too easy.

A JIS driver will not damage a Phillips screw head (but the reverse is not true). I only use JIS drivers these days for that reason.

Manual JIS drivers exist up to #3. A JIS driver might help but I know of no reasonably-priced source.

Those screws may be sloppily made too. A JIS driver may not get any additional bite if the head cuts are not made to Phillips (or JIS) standards.