Quoted:
Sounds like what your hearing is "Turbo Chuff". Which is caused by the turbo putting out quite a bit of boost to meet power demands, and then getting out of it really quick. The turbo has no where to put the boost as you slowed the engine down, so it "chuffs" out back through the intake.
I had my 6.0 up there for a couple winters while I worked in Williston, and I run Shell Rotella T6 5w-40 Full Synthetic. A lot of guys run the Chevron Delvac or Delo oil and have good results. I personally use Rotella because I like it, and after all, quality oil is pretty much the same these days.
Give me a few and I'll find the chuffing videos on youtube for you.
EDIT: After re-reading your post, it almost sounds like maybe the vanes on the VGT are sticking. That would be a good explanation for your poor acceleration off of the line.
For your battery woes, I would take a multimeter and check your DC and AC output on your alternator first to make sure its putting out correctly. After initially starting the truck, you'll have to let it run for a couple minutes as the BCM doesn't turn the regulator on until after the glow plugs have turned off, and on this model engine, the glow plugs can run for around a minute after being started with out the glow plug light actually being on. Granted, its pretty warm in ND right now, but something to watch for.
As for checking AC voltage, I only do it to check the health of the diodes inside the alternator to ensure it's in good condition. Typically, if your AC voltage is over .25 vAC, you should start looking to replace the alternator.
As for it being the catalytic converter, I highly doubt it. I've seen a couple get clogged up, or break free inside and cause issues, but it would be a full time power loss issue, not a part time. You can straight pipe it though, they sound pretty cool afterwards
Now with all that babel out of the way, you probably need an alternator. The stock Ford one is not really that good of a product. There's a really good aftermarket one that is out there made by DC Power Engineering.
https://www.dcpowerinc.com/
I have a 190 AMP stock replacement from them, and I must say it is a quality unit. Not especially cheap, but it's good stuff.