First off, there is no way to know how many points you'll lose for inq. I've lost anywhere from none to 5 points for 2 inq on same day. I've lost more points for util reporting than an inq. So, I wouldn't worry about losing a ton of points for your inq.
Barclay's is a unknown. As others have said, it's YMMV. IMO, keeping your util LOW on all your CCs will counteract any concerns they have about your getting new accts. That said, 6 new CCs is a lot. There's just no way of knowing. But I would PIF any balances BEFORE your statement cuts on all but one or two of your CCs. And those should be under 10%.
If they do close your acct., it wouldn't have any effect except on your util. With a 500 CL, the effect on util is minimal. It will continue to affect your AAoA for 10 yrs.
Speaking of AAoA, that's going to be your biggest FICO hit. I just lost 14 pts for a new acct because it moved my AAoA to under 5 yrs.
EQ FICO 750 | TU FICO 761 (Walmart) | EX FAKO 767 | Goal: 800+
Edits, funky spacing and spelling due to my iPad not getting along with the forum editor!