I'd replace the frame, if this were mine. You could simply use a non-"numbers matching" frame to hang all of the same parts and you'd have a structurally sound version of the same bike. Only real difference is the SN. I don't recommend transplanting VINs, that's just asking for trouble. OTOH, it IS perfectly legal to use the VIN on an unstamped, service replacement, Honda frame. That was done back in the day, when it was necessary to reframe a bike. Those NOS frames are scarce. Alternatively, you could take your time and shop for a suitably-number replacement over the winter...or someday, and just enjoy the "mis-numbered" resurrection of your beloved bike.
As for the battery acid causing the damage, it's certainly possible. It's also on the unusual side. That's an odd location for a major rust-through. And Battery electrolyte dries out quickly, in the open air, after which it doesn't do much. I'd bet that there's more rust erosion inside your frame than just what shows in the pix. Most of the acid damage I've seen over the years has been to the internal heat shield and perforations are rare. It's horizontal surfaces that are most vulnerable; vertical surfaces dry quickly and "see" less exposure. I've run across a few heavily rusted battery carriers, never one that was unusable, even the worst. Most of them just get pitted along the bottom. Even with vintage cars, rotted-out battery trays resulting from battery leakage alone aren't that common. In an automotive setup, the tray acts like a shallow pool and car batteries hold more than enough liquid to keep the metal wet, with unused (any given quantity of sulfuric acid can only dissolve so much metal before it's "used up". The missing elements...moisture and time. If this is the same frame that held the 4-speed engine, it saw eons of prolonged moisture exposure. Your engine had the most rust & oxidation damage I've ever seen, that could still be brought back to life. At one point, I wasn't sure there was enough metal left to recut the valve seats properly. The stator O-ring sealing surface was really bad, too.
Doesn't mean I recommend using an OE-style leaker battery. There's no good reason, other than display, for that circa 2020.