What about compression? Consider a simple compressed archive file format:

The first four bytes of the file are a 32-bit unsigned value representing the number of files in the archive. The rest of the file is the contents of the file (all files in the archive must be identical). The original file names are stripped in this format and are undefined in this standard, but they can be assigned at unarchival time using a method determined appropriate by the implementer.

As an example, a hex dump of such an archive of 10 files, each containing the string "Welcome to Hades." might look like this:

00000000: 0a00 0000 5765 6c63 6f6d 6520 746f 2048 ....Welcome to H
00000010: 6164 6573 230a                          ades..

If you convert 300,000,000 empty files to this archive format, you end up with a 4-byte file containing:

00000000: 00a3 e111                               ....

Assuming a 1440K 3.5" floppy using a filesystem with high overhead, say 32K + 4K per file and a 4K block size, this would fit with 1400K to spare.

Using the same filesystem assumptions, how many files can we put on a floppy disk using this scheme? The maximum we can store in a single, one-level archive file is 2³² (~4.2 billion) empty files:

00000000: ffff ffff                               ....

However, to mitigate filesystem overhead, we can take 2³² of these archives, each containing 2³² files, and end up with an archive storing 2⁶⁴ (~18 quintillion) files in 8 bytes:

00000000: ffff ffff ffff ffff                     ........

An so on! Using this method, we can use our 1404K (capacity after filesystem overhead for a single file) to store an archive file containing 2^11501568 files. This is such a large number (~10³⁴⁶²³¹ ) that there's no good way to put it in perspective. Quantities like this do not exist in nature, and yet, we can easily store that many files on a floppy disk. Of course, this is only one way, and there are compression schemes which yield infinite file density.