Eutectic overloads can be ruined by resetting them to soon and or repeatedly. AB were notorious for the alloy separating. I picked on AB because those are the ones I am most familiar with.
So a LONG time ago, the old "N" type OL heaters had the solder pot and pawl in the relay base and just the heater element was placed over it. So if people got annoyed with nuisance tripping, they'd keep increasing the size of the N heater element until they would literally cook away the solder by over heating it until the seal on the pot case melted (let's leave out the motor damage issue for this). In the early 80s, A-B changed to the "W" elements, in which the solder pot and pawl are on the replaceable element part, the relay base only holds the ratchet and contact mechanism. So when you replace or increase the size of the W heater, you are also replacing the solder and pot, therefore repeatedly trying to make it fail is less likely to succeed. The motor damage still happens of course...
Back to the OP's question, the reset time, which for a eutectic is the solder solidification time, is part of the eutectic alloy preparation, specifically to match the cool-down rate of a standard NEMA spec motor. You cannot* make it reset any faster than it is designed to.
*That's not meant as a challenge... I suppose with some cold spray or something exotic like that, you could.