Wow, exactly the kind of thing I was looking for posted in 3 minutes. Amazing!

It goes into pretty poor detail on the actual medium itself, unfortunately. How fine were the particles? What was the exact recipe that worked?

Some of the commenters had much more interesting things to say:

::: spoiler @verdatum

As a kid, the thing that blew me away was Tim Hunkin's The Secret Life of Machines. He had an episode on the cassette player/recorder where his partner demonstrated that cassette tape could be emulated by taking Scotch tape patting it into a or iron-oxide and running that result over the tape heads. "This is the sound of my voice recorded on sticky-tape and rust." that revelation absolutely blew my child mind. ::::

::: spoiler @DerWahreTee

I might be able to give you some advise here. I am a material chemist and I professionally work on polymer coatings similar to the one your using. I think your problem is at least partially a poor particle distribution and uneven coating thickness. The particulate you are trying to suspend needs to have a particle size <1mikrometer. When you buy such particles as a dry poor they have agglomerated during the drying process I.e. they have become stuck together in unevenly sized chunks. This creates also makes the particles less evenly spread throughout your coating than it visually appears. To break up these agglomerates you actually need a tremendous amount of kinetic energy which your magnetic stirrer can not do. Also the Mayer-bar isn’t really the ideal method to apply your coating even if you can’t see it it is notoriously uneven on a microscopic level especially when applied by hand. Ideally you would use a spincoater which could apply you coating more evenly. Hope this helps :::

::: spoiler @fiscap Commercially produced floppy disks go through a magnetic alignment process, while the coating is still wet. I think the magnetic particles in your solution/suspension are too random to produce a consistent and reliable flux transition during the write process. If you do try this again, try to figure out a process to align the particle orientation and keep it in place until the coating fully cures. :::

::: spoiler @stamasd8500

I am pretty sure the magnetic material that you used is part of the problem. You don't give a lot of detail on what exactly you used, but in the video you say "black iron oxide" so I infer you used magnetite, Fe3O4. That is not the correct material to use. I did some research not long ago into magnetic materials used in the period, and even recreated some magnetic material after poring through some research papers and patents from the 1950s to 70s. The magnetic material used on floppy disks is a type II or III material (as defined for magnetic tapes) so either a cobalt-doped gamma-Fe2O3 or a chromium dioxide-based material. Magnetite is not correct as it doesn't have the required saturation flux and coercivity. I have in fact recreated in my basement lab a type II material, a cobalt-doped gamma-Fe2O3 ferrite which would be appropriate for that. It's not difficult but it requires patience and precision. And a few tools, including an electric oven that can go to at least 850 degrees Celsius. :::

The last one gives me one possible place to search next. What are the numbered material types referenced?

Anyway, if it weren't for the sponsor, the way to make the substrate would have been just a punch, right? Laser cutting and then baking the sheets flat again felt a little unnecessary.

Hmm, all the way up at 1mm. Man, that tape length really adds up, doesn't it? So, to the question exactly as I asked it, I guess obviously yes.

Maybe I can do even better then. If I'm also building the head, the dielectric gap that does the reading and writing can probably be as small as tens of microns, since you can fairly easily make an edge that fine. Keeping the tape clean and even enough to not crash would be hard in that context, though, since it seems like clearance needs to be on a similar magnitude. Does anybody know what consumer tape reader/recorders use?

In tape form getting an even layer of medium might also be challenging, although if I went with a disk instead it could be spin-coated. Highly oriented particles sound doable with a bit of chemistry.

I'd upvote this, but ironically it would make it look like I didn't upvote it.