As some others stated, I did not remove the cable assembly from the shield either. It looks like it would be difficult to do without tearing.
Since I don't have a microwave, I couldn't use an iOpener. Instead I put a hair dryer on high and aimed it at the front of the screen for about 10 minute and was able to pop everything off. If you do this, don't do it near where you've taken the phone apart since the hair dryer will happily blow the screws you need for re-assembly far away.
When Re-assembling the whole thing, there are tabs at the top of the screen that need to fit into the top of the metal case for the whole thing to close. I found this to be one of the trickier parts - if they don't engage properly, and the rest of the case seats, the screen doesn't lie flat and you need to go back to the suction cup to separate it again. Look at the inside top of the old screen under a bright light before doing this and it will be easier to understand how it engages.
When opening the front of the phone, there are two pieces of the front assembly the go to the edge - the glass, and a thin piece of plastic that sits behind the glass (and provides an edge). The glass is flexible enough to bend, leaving the plastic behind in some places. If you pry between the glass and the plastic, you will end up breaking the plastic. In my case I was replacing a cracked screen in addition to changing the battery, so this didn't really matter much since the plastic part that broke was part of the new screen assembly. But if you're just changing the battery, make sure you're prying up on the plastic as well as the screen.
I was not successful at getting the adhesive tabs to release the battery so had to pry it up with a spudger. If you do this, be aware there are device cables glued to the rear of the case near the top 2mm or so of the battery.
Finally the article notes potentially using tape to hold the battery - foam tape is too thick for this. I used no tape at all without issue.