Regarding your question, G/S coverage is provided at least 100ft below your cat I minima.
Taking into account the desensitization of the G/S mode bellow the minima, for an average speed of 140kts, 2 possibilities exist to trigger the warning :
1st to be in the lower limit of the envelope just before the minima and diverging (G/S déviation not meeting the stabilized app criteria).
2nd Being on G/S passing the minima and increasing the V/S above -1000ft/ min (unstable approach below minima).
Triggering the G/S mode at such low heigh means, that you do not comply with either the visual aids (Papi/ vasi lights, aiming point) or the minimum threshold crossing height (RA).
I agree with you that below the minima and with positive visual contact, you can “adjust” your flight path in order to touch down as close as possible to the aiming point. Nevertheless, I always respect the minimum threshold crossing height of my type(did you check yours?).
You didn’t mention if the situation occurs during a special type of operation (LDA performance limited field) or if it is just a way to vacate the runway earlier.