Call for information on virtual tape formats 355
I recall a card-resident dump program for the S-360 model 44 that could dump all of main memory, including the low-address goodies. The basic 44 was a stripped-down S-360 that did not implement all the instructions described in PofO. There was an extra-cost add-on that gave the 44 the ability to emulate the missing instructions; it amounted to a bag of normally-unaddressable memory plus some extra goodies to divert "invalid opcode" traps to an emulator that resided there. (There was also hardware to implement a few of the missing instructions directly: Load Multiple and Store Multiple were among them, and there may have been one or two others.)
The extra memory was not even addressable by the I-O channels, except when a special "emulator IPL" button was used -- and that, of course, is how the dumper worked. You put the deck in the 2540, dialed up 00C, hit "emulator IPL," and the dumper program got loaded into the extra memory leaving main memory intact. There were a lot of things you couldn't do while running from the emulator memory, but one thing you could manage was to use the DIagnose instruction to move data between the two realms. So the dumper copied some stuff from main memory to extra memory, then copied itself to main memory, issued a couple more DI for some mode switches and stuff, and could then proceed to do I-O for the dump.
Call for information on virtual tape formats 356
I think that you'll find that in many cases tape drives will read the short records if everything goes well, but if anything...
(Fading memory: I'm pretty sure the "emulator IPL" button didn't have that exact legend on it, but I can't recall what it actually did say.)