Sambo, I just called this morning to do the very same thing. My Rewards card has a much higher limit, but the Apple Card I was approved for was a little lower. I called in today to recon to move Apple Credit limit to Rewards card and close Apple, and they increased my CL. Also offerd me the option of closing and moving CL or increasing credit limit. I accepted the credit limit increase.
I too, was concerned about calling them because I just opened 7 new Visas and Mastercards last week (all with high limits, so I'm a bit in shock- didn't quite expect). I've had a very good relationship with Barclay's thus far and did not want to mess it up.
A couple of inquiries had hit TU and they could probably see one new account, but not everything is showing yet. I think it's best to call them now if you are going to before all of your new accoint show. I udnerstand your fears aout inquiries and the new accounts. I have found with my Rewards however that as long as you keep your overall and individual utilization very low, use the Barclay's a lot nad make large payments, they didn't do anything crazy like AA. They just seem to like to have the usage and know they are special to you. 