Destructive devices were not addressed by the NFA of 1934. They were completely legal to own, shoot, and order by mail until the GCA of 1968 when they came under the purview of the ATF with the newly defined "Destructive Device" class of weapons. This also addressed the ammunition fired in these guns, which was also previously legal, including high explosive ammo.
These differ in definition from a machine gun, which can be the whole gun or just the bare receiver, either of which is an NFA firearm in the eyes of the BATF. A destructive device is a combination of parts, generally a receiver or breech ring and a barrel larger than .50 caliber. A bare receiver from such a weapon is no different than a normal shotgun or rifle receiver, and not subject to NFA registration. So you take a 105mm howitzer breech ring and attach a .30-06 Springfield barrel with a big, fat sleeve......legal, and not NFA. Take a 105mm howitzer barrel and attach that same breech ring, or somehow attach that barrel to a 1903 Springfield receiver......NFA registration required via Form 1.
The concept of how a DD is defined is important when considering what to do with odd things found in the attic. If there is no barrel present, there is no DD. The receiver and all the rest of the parts can be owned without any more restrictions than a rifle (in most states). You could certainly take a Lahti or Solothurn receiver, file the Form 1, find or make a barrel, and put your new, legal DD together.
I'm sure, in the 46 years since the GCA of 68, a few unregistered DDs have been found that had their barrels removed, papers filed, and then reunited with the rest of the parts. Officially, that is prohibited by BATF as the barrel should not come from the original receiver it was mated to. In their view, if the gun exists as a complete assembly, it's already illegal and subject to confiscation. Just remember that when the forms are filed, you are essentially certifying that you only have half of the total and are looking to find or make the other half. If you already have both the barrel and receiver, you are in constructive possession. And if the original barrel miraculously appears and gets reattached to your receiver, a later inspection by a saavy BATF agent might just produce some difficult to answer questions like...."I see the fit, finish, and serial numbers match on this 20mm cannon you manufactured on a Form 1...how is that possible? Where did the barrel come from?"
So yes, it can be done, and big, heavy chunks of cannons don't necessarily have to go the torch. But there are pitfalls and difficulties to negotiate along the way.
By the way, I don't remember the details but recall there was a batch of 20mm Lahtis that were sold in the1980s? that were rendered unserviceable and sold on 4473s like a rifle. I always assumed the barrels must have been pretty well destroyed or BATF would have required them to be sold as Unserviceable Destructive Devices, still requiring NFA registration, but without payment of tax. Struck me as odd at the time but never dug into the details as I wasn't a Lahti guy. The Solothurn guns all came in Pre-68 and were all live when sold. Like the Lahtis, a lot of them got registered during the 1968 Amnesty, but a lot of them didn't, either because the owners never heard about the requirement or were afraid of the Government and didn't trust them.