Panic-And-Lose-O-Matic is a way of life for them. If Apollyon found a way to try and use a particle accelerator to turn Terra into a black hole, he might do it as an expression of Blake's Will, let alone a hyperpulse gun theory.
They did actually have a system for nuking Earth, the Operation MEGIDDO, as detailed in Final Reckoning along with the HPG cannon. They didn't end up using it. I mean, someone at the top did order its activation but that didn't go through, just blew up the Hilton Head Island, probably in an attempt to prevent full activation of the system.
Since the Republic captured a lot of Word of Blake tech, i'd imagine they would've obtained the HPG cannon were it real, or at least actual technical data, and given the dire straits they're in, i would assume they would've tried the weapon if it were in their possession (they did try stuff like RISC tech after all and deployed the Fortress which was supposed to be a emergency contingency). OK, it is possible it got blown up, but bunch of other hyperspace tech didn't: i'm pretty sure the Blackout and the Fortress are derived from Word of Blake tech and theories, that faction was the leading hyperspace researcher after all. As such, i'm really doubtful the HPG cannon ever truly existed.
As for other WoB superweapons, we have pretty good overview of the WoB projects in Final Reckoning. I can believe they also had projects for more conventional tech as well, and i wouldn't be surprised if some were used (subject to future stories, if any will be written ever). But for super-advanced tech, i'm thinking Final Reckoning got them all.
And i am sure they would've tried bunch of them, if they ever got them to working prototype status, even just one example. For contrast, the Clans (Vipers?) apparently deployed some kind of super defense or armor on a WarShip during the War of Reaving, evidently one of a kind. That definitively does happen in real world and Battletech universe, and there may not be evidence left behind, but the HPG cannon doesn't feel like a similar example, i interpret the text on Final Reckoning as the Word of Blaking supposedly having more of them and that Apollyon just had one installed on his 'Mech.