I'm trying to change the way I pick based on what everyone tells me, but unfortunately everyone tels me something different and the three ways I try all have advantages and disadvantages. I tried between my thumb and index tips with anchoring my pinky, without anchoring, and the Paul Gilbert style with the pad of your thumb and side of your index. Anchoring is what I did for the longest and is the most comfortable, but it tires my hand out after awhile of playing. That without anchoring makes me lose some accuracy but cuts down a little on strain. And the Paul Gilbert thing definitely lets me play scales the fastest and has the least strain, but it's extremely awkward feeling and makes it hard to do simple things like tremolo picking and palm muting. It also seems that no matter how I this one, my tremolo picking is very quiet compared to the other ways.

TL;DR: What is the most recommended way to hold a pick, and how long should it take to get used to holding it a new way.
la de da.
Just hold it however it feels the most comfortable, there is no correct way, but there are different ways to hold it to accomplish different effects. Like partial artificial harmonics, requires you to hold the pick very close to the tip.

It's all preference dude.
I know, but the different ways do help in different areas and I wanted to know which one will help in the most ways, and have the least chance of, say, carpel tunnel
la de da.
Well, I hold my pick using my thumb and pointer finger, and have the rest of my fingers resting on the bridge, but I'm a rhythm guitarist and like my heavy palm mutes.

I mean, however you can hold the pick will work, if your looking to improve on technique or accuracy then I can't help you there, I just normally don't stress over it.
If it hurts, you're doing it wrong man

There is no one way to pick the string, but the most important thing to advancing at guitar is relax. Tense muscles cause injuries. Just do what feels comfortable.

Also, if you're worried about artificial harmonics, you can do them with your ring finger instead of the tip of your thumb.
Artificial harmonics are the least of my concerns. But there is absolutely no completely comfortable way to hold it. If I relax enough so there's no strain, I'm basically not even holding the pick anymore.
la de da.
try finger picking?

or just experiment till you find a comfortable way to hold it.
Quote by Dirk Gently
Some pieces are only meant to be played by people with six fingers on their fretting hand. Sorry.
if it feels good its right. if it feels bad it could be harmful. do the one that feels more comfortable and just work on stamina.
I'm basically not even holding the pick anymore.

You don't need to hold onto the pick very much. Seriously, use as little of the pick as possible and a hard pick and you'd be amazed how little you need to hold onto it.

The main thing that worries me is that you seem to think your tremolo picking is "different" to your picking for scales. They're both just picking notes.

If you're using a kind of "spazz arm" technique for trem picking then that's probably a much bigger problem than holding the pick or anchoring.