Ahhh, so your house is on a slab PERIOD, with no foundation walls! In that case, you were right to remove no more soil.
To anchor the sill plates into a thinnish slab, I'd be very careful about how I do it. Start shooting Ramset fastening and what you may do is chip off chunks of the slab edge. Not good.
I'm wondering if the sills need to be anchored at all. Normal anchor bolts into foundation walls resist uplift and sliding forces. Uplift comes from wind passing over the roof and creating a low-pressure area there, which causes a house to tend to lift. It's pretty much got to be hurricane-force winds.
Sliding forces come from wind (relatively small) and earthquakes. I don't think you are in a serious seismic zone there.
Any of those forces, if strong enough to matter, will probably be strong enough to break the slab and allow the house, anchors, and bits of the slab, to move, so the anchors probably won't be much help.
There are hopefully enough anchors in the side and back walls to hold the house, and I'm thinking, why worry about the front wall? I know structural engineers reading this will be having cows, but that's what the not inconsiderable seat of my pants tells me.
Were you able to toe-nail the studs to your new plates?
Architect (NY) and Home Designer (PA)