So my question is, what is the deal with these chips and why do they seem unique to this particular interface card?
While the orange colouring is quite flamboyant, the use of hybrid circuits/modules was, and sill is quite common. Although, the colour was not specific to Hayes, but of Sprague Electric (today part of Vishay). Also, they were used on several variants, including IBM-PC or S100:

(Taken from the S100 Computer site)
It almost looks like they were an epoxy protection scheme, but I don't think there was anything really top secret about the device.
No, it wasn't. The lacquer layer is to protect the components placed on the ceramic substrate against mechanical and electrical damage.

(Taken from Wikipedia)
Hybrid devices are all about miniaturization. In fact, they are the genuine Integrated Circuits, or ICs, predating today's use of IC, which were called Monolithic IC at first (*1). IBM's Solid Logic Technology (SLT) for example used hybrids to package several transistors and resistors into ... well ... integrated circuits for their new /360 series. Enabling extreme compact boards and as well to reduce cost.
For digital functions, monolithic ICs did take over soon, most notably with James Buie's TTL design, popularized by TI 54/74xx series. For analogue devices, hybrid technology was and still is the way to reach higher integration - although development of ever finer board production and advancement of SMD with devices as small as 0401 is taking of more and more areas originally held by hybrid.
As well, I would think there were non-blobulous versions of what they needed available at the time?
A rough comparison can be made when looking at the stand alone Micromodem:

(Taken from Wikipedia)
Comparing the external Micromodem to the Apple II version of less than half the board size (note: pictures are not scaled accordingly) shows how crucial the use of hybrid circuits was to make it fit.

(Taken from the question)
I would be interested if anyone ever "decapped" (or just melted them down) to see what was inside.
Since the content was part of the description, it's less work to just look at the schematics.
*1 - Hence several early IC makers carrying the word 'Monolithic' in their names and all of them on their data catalogues.
Hybrid IC... – Spektre Oct 23 '22 at 06:36