xcode 7.2.1 install taking a long time

I am on a Macbook Pro, 2.8 GHz Code 2 Duo, 4GB 1067 MHz DDR3, running OS X 10.11.3 and it's up to date.

I am trying to upgrade XCode to 7.2.1. First, I tried using the App Store, but that hung literally overnight and Launchpad was no help either. So, I downloaded the install package from https://developer.apple.com/downloads/. The download didn't take very long, even though that's a 4.73 GB download.

However, it took a couple hours to mount that dmg, then overnight to install (i.e., copy the file to /Applications), and then it took 30 minutes or so to launch (verifying Xcode.app), and then it hung without fully launching. I killed it and restarted the machine. Now it's verifying again - its been running for 15 minutes or so and the progress bar is not quite half way through.

I have downloaded and installed a few other things (none were as big as XCode) during that time without any slowness at all, so I don't think it's the computer.

I get that SIP is part of the system, but does anyone know why this is taking so long?