most meanwell power supplies in the series you’re referencing come in the gsm and gst versions. the number later in the model number indicates voltage (12 vs 15 vs whatever). if you look at the pin assignment portion of the datasheet, it will typically indicate if -v is connected to ac frame ground (which is recommended for some capacitive touch modules to work properly).
it is important that you look at this for the exact adapter you are considering, since the t and m designations are inconsistent with respect to grounding scheme across the line. typically in the lower amperage/barrel connector adapters, -v is connected to frame ground in the gsm version.
so, in your case, a direct replacement for GST40A12-P1J would be GSM40A12-P1J, which does have -v connected to ac fg.
to answer the question "Would it hurt to swap a Meanwell GSM60A15-P1J for a GST40A12-P1J to see if it solves a power problem? ", that depends if the erica synths travel case power supply can accept an incoming voltage of 15 volts instead of 12.