TL;DR change the speakers don't fuck with the cab.
If you're thinking about changing speakers, I'd do that first. I say this for a couple reasons. First, Fryette is a good manufacturer and I'd be hesitant to mess with their designs, just like I'd hesitate to slap wood on the inside of my Bogner cabs. Secondly, wood is the last thing you wanna fuck with because it's the hardest to reverse. You can change speakers 100 times, and go back to the original V30s and have that cab 100% restored to original. Tack on some wood, and you've at a very minimum have scarred it even if you can easily reverse it.
To further encourage you to explore speakers, that will impact your tone MUCH more significantly than a brace (anyone here who has actual experience, please correct me if I'm wrong. This is more of a hunch tbh). If the V30 is _almost_ perfect, then maybe a tweak to the cab is right. But I'd advise trying other speakers first. For instance, I had my mind made up that I would never like Greenbacks. "They're vintage... They're not good for metal... they'll fart out if you have too much gain..." Dude, I have fallen in love with my EVH-signature GB Heritage loaded Bogner. Granted, I only love them when the master is dimed. But my god the lows are one of the sorta things like you wanna have in your sex life.
To finally basically just say "dude, you're stupid if you don't try speakers first", my DOC when playing with anyone else is V30. GBs are for my alone time lol. Unless you have a setup where you can politely dime the amp, you'll have to dial the master back and those GBs lose their sexiness because it's so influenced by speaker breakup. They grow a bit "cold" to use the term guys throw around about GBs, which just so happens to play into my sexual analogy too. Plus, if you're jamming with someone other than only a drummer, then you'll learn that V30's are the way of saying "Hey y'all, here's my god damn contribution to this music" because those speakers have that upper mid that CUTS. Any mix. You're gonna be heard. So I've learned that I love my Bogner as my base cabinet, but I have different speakers for different situations with all the exact same gear.
I'm kinda laughing that you are struggling with V30s having tight low-end, btw. The Bogner that has the Marshall-labeled V30... the low-end slays so hard, I'm planning to start tampering with power tubes or even taking it to the builder to rip some low-end out. It's so huge and tight. Maybe what you need is a Bogner cab instead? LOL
Jokes aside, have you tried G12-75 Celestions? I just picked up a Marshall loaded with them for shits and giggles. The low end is overwhelming. You'd probably love it. And I'm sure you've noticed they're popular to mix with V30's in an X. So with $150 you should be able to find a pair of worn-in V30s (or Hellatone 60s. Same speaker with someone else's label) used. Just make sure you know the correct impedance to purchase.
Funny thing about that too... My first Bogner was V30s when I bought it and I mixed in two K100s. I never loved it. I tried it forever, but never loved it. Thankfully I stopped being stubborn about my speaker choices which were based on reading stuff people like me write to waste your time, and started trying speakers and found all kinds of cool shit I'd never figured out by reading.
Oh, so change the speakers and don't fuck with the cab.