I'm a big fan of them, so it would definitely help if I could mimic their style. I'm still learning, but I want to be as good as them one day.
Excellent... and brave.
I'm sure you already know this, but if you gave Herman Li a few hours to setup your Squier himself, he could shred on it all day and sound just like Herman Li. This is something that is just generally true of most any decent musician -- they can sound amazing and sound like themselves with any PoS instrument. I didn't need the following video to understand this fact (I learned the hard way), but the fact that he's shredding on a $150 Squier helps drive the point home:
https://www.youtube.com/watch?v=hwztSlWXcfM
What is also true, is that there are guitars on the market that are better suited to shredding than a standard-spec Stratocaster. I didn't see Herman do too much with the whammy bar in that vid, and I'm sure that's a deliberate choice based on the limitations of the instrument AND what he feels is important for earlier-stage players to focus on. I love that he makes it clear: "you're not going to be playing Dragon Force songs if you're just staring out".
As to when is the right time to move on from your Squier and get a guitar with more shred-friendly specs, that's a personal decision -- don't let strangers on a forum steer you.
That said, my 2 cents is that you take the time to understand your current instrument as best you can before you go shopping for your next guitar. You'll need this understanding in order to make a good purchase decision. The fact that Herman goes right to his workbench and shows you how to do a full setup on the guitar, in a video aimed at beginners, is 100% on-the-money. Please don't skip over this stuff, it's essential to learning the instrument. Herman is a Gen-Xer like me, and had to learn the hard way: reading Guitar Player Magazine, watching tedious instructional VHS tapes, and playing along to Dave Mustaine on cassettes and CDs. Rather than telling new players to suffer like he probably did, he's trying to make things faster and easier, which tells me he's probably a pretty decent dude.
The fact that you're asking about your Strat going out of tune leads me to believe that you're still learning the differences between a standard-Strat floating-bridge tremolo and a Floyd Rose locking tremolo system like Herman has on most of his guitars. Herman has teachings on this topic too, of course:
https://www.youtube.com/watch?v=dyzTJ-R89KI
A more shred-focused guitar isn't going to make you a better player in any way, of course, but if the instrument makes practicing the kind of music you want to play easier and more enjoyable, it might be worth it. Most of your tone is going to come from your amp & FX in these styles, your instrument's job is to fit your hands and playing style like a great pair of shoes.
So, at the risk of being wayyy too presumptuous, and a huge windbag, I'm going throw this out there:
When you can walk into a guitar shop, and tell the person working there the following, and you're comfortable with what each of these things means, I think most would agree that spending $$$ to upgrade is warranted. You may already be at this point now, but here it goes:
"Hi there, I'm looking for my next electric 6-string. Among other styles, I play a lot of Power Metal, and I want something that's more shred-focused than my current standard-spec Strat. I'm looking for something with:
- A Floyd Rose-style locking trem system, or similar, as I intend to use the whammy bar A LOT, and my Strat's standard trem goes out of tune too fast
- 24 frets with good upper-fret access
- A flatter fretboard radius and jumbo frets to make it easier to play high up on the neck
- At least one humbucker, for a chunkier tone
- Most importantly, I want a well-made guitar that can give me lower string action with a minimum of fret buzz, so I can move around the neck faster
I'm pretty set on Ibanez, because Herman Li is an influence of mine, and he's been happy with a whole range of different Ibanez guitars throughout his career, but I'm open to anything that is geared towards this kind of playing.
I realize the player's hands, talents, playing style and amp/FX choices dictate tone way more than the guitar itself, but I practice every day and I want my practice time to be more comfortable and enjoyable for the kind of music I'm into.
Also, as this will be my first guitar with a locking tremolo system, I hope your in-house tech can show me how to re-string and tune the guitar. I've watched videos and know what's involved, but I'd appreciate a hands-on demonstration too, if possible."
If you're all set one what each item above means, and you're confident a better guitar would enable you to practice more comfortably, you're ready for that next step, IMHO.
... but, again, I'm just some forum stranger who types too much. I haven't even owned a 6-string in this century. Take my words with a grain of salt.