I still own a Para-Ordnance P12.45 and I have owned a para 12.45 LDA (both now, unfortunately, discontinued). Both have been completely reliable (disclaimer: The P12 was bought well-used and obviously "broken in." The 12.45 LDA gave me a lot of problems in the first 100 or 150 rounds. Once I realized I was shooting junk ammo and switched, ALL problems went away.)
I do not own a "Fatboy," but I have handled one. I don't like the fact that there are no grips that can be changed, but the rest of it looks good. The manufacturer (Shooters Arms Manufacturing) has been in business for a long time and they make good 1911s. If the Fatboy rings your chimes, I think it will prove to be a reliable firearm.