And here I am again to save the day and give you your best answer. Outside of Special Forces units, the only straight up 11Bs on jump status in the National Guard are those assigned to the Charlie Troop (Long Range Surveillance) in Cavalry Squadrons of the six Battlefield Surveillance Brigades. For example, Indiana has one.
I know this, because I am assigned to one. We were just doing home station drill (not going to the field) so just to stay current, all the guys on jump status show up at our armory, they load up a C-130 or two and then fly them back to the small community where they are based out of and have an authorized drop zone and then jump in. (This guy is new to the unit and waiting for jump school) This is combined with additional training for schools and identifiers, MTOEs that have lots of ASIs. Many NCOs in units like these come from former SOCOM in active duty or have been willing to make the extra time commitment to go to extra schools (Pathfinder, Sniper, Ranger, etc) to stay sharp. There's a bigger commitment than just one weekend a month and two weeks a year to maintain proficiency in those skills. However, don't think that it can't be done just because it's not active Army. The Active Army wastes A LOT of time during the year because you can't be in the field all the time. It's too expensive and people have to have families.
Anyway, more elite units like these draw and select people who are more intelligent, more motivated, more experienced, etc and are highly effective. If you have one within commuting distance, I recommend you get in touch with them and ask to interview.
Edit: I am not talking about entire Regiments. I am talking about full Troops (company sized) of Infantry that specialize in reconaissance. All the slots for entry level are 11B1P which is an Infantryman parachutist code. This is the same for any entry level Infantry position in an active unit. I also missed part of your question earlier. Although no units are designated as Air Assault, the Guard gave up several of its armored brigades in exchange for light Infantry over the last couple years and has opened its own Air Assault School at Fort Benning to handle the influx of National Guard soldiers attending Air Assault. If you're light Infantry, you will likely be given the opportunity to go to Air Assault school and your unit may conduct helicopter operations as needed. It's hard to say.