The Regiment detachment is amazing, don't get me wrong, but it only really becomes properly
amazing in games larger than 2000 points.
At this level you're better off not having the taxes and taking nice big units of everything (we're talking thirty men, ideally) and taking more of an advantage from our natural special rules. Big units that stand still and have a general to buff them are much better off than tiny units with the buff from the Regiment. I mean your ten man crossbow units won't last long and don't stand a chance while they do.
I'd say consolidate your list into bigger infantry units, maybe bring another general, and maybe drop some of the Demigryph Knights (they are great, but not that efficient) for possibly some Ironweld Arsenal support with Helblaster guns and a Gunmaster. You want a Nuln theme right? Nothing will give you better peace of mind than a steam tank rolling up your enemy's flank.
You have a good start for a Regiment detachment, it just needs to be bigger.