The 'this is how I've always done it' may be true, and other engineers may have even justified a similar scheme in the past. I know I have. But there are always seemingly small items that can change everything. Have checked a similar situation to what you're talking about recently, 6" PT slabs on PT beams spanning a bit further than you. But load on the shoring I've looked at is more like 13k after being shared between a couple floors, not 17k, and only 20" or so away from the edge of beam. Negative moment under shore force is a little bit lower than it would have been for just the live load distributed over the shore spacing. Doing a quick hand calc based on a two span condition, if you make that 36" away from beam instead of 20" then my negative moment increases 60%. Doesn't seem like much to a contractor, so he'll say he's done it this way before. Doesn't understand how taking a half step to his right means the difference between the shoring scheme working and the shoring scheme being nowhere close to working.
One thing I'd question a little further is this only getting reshored one floor as you've noted. If you're pouring a 5" slab, you're looking at 63 psf of normal weight concrete plus formwork/shoring and personnel loads. Would think all that would tend to come out at 2-3x higher than your typical 40 psf passenger car garage load that the floor would be expected to support in addition to its own weight. Unless garage was designed for a much heavier live or finish load or seriously overdesigned. Could be fine and I'm just missing something, but doesn't seem quite right at first glance.