Many thanks to all who gave me encouragement and advice on this one. I got in a little time yesterday, and took the Maserati GS for a spin. The build was in spec for this challenge already, and I had an old tune on it that's probably just a F'dog.
I don't know why, but this car just seemed to agree with me. I tried to apply all the advice I received on here (except I hadn't yet seen Hop's suggestion for backwards mapping the track; I'll have to play around with that), as I ran a few laps without being overly concerned with my times; concentrating on my lines, throttle control and apexing instead.
After about a dozen laps, I hit 117.041 with more to be had. That's still way off you guys, but that's full second and a half below what I was running with the Xfire. I chalk it up to getting more familiar with the track, plus focusing more and actually not stressing about it. (This is supposed to be fun, right?)

Anyhow, I'm thinking about going back to the Xfire for a while just to see if I'm really driving better, or if it's just the Maserati.

But for now:
Maserati GS: 117.041 Chuck