One way for you to create an install media with the firmware included: you can install antiX-M8.5-beta4 to a usb flashdrive using antix2usb (Control center > Disks > antix2usb). It automatically installs a frugal and persistent system, i.e., a system that boots from the live iso but retains all the changes made by saving them on a persistent partition.
Having it installed to the flashdrive, boot it on a machine that has a functional Internet connection and install the firmware you need.
You can then install the system from the flashdrive to your laptop and it should carry all the changes you have made to the new installation.

Also, any advice on the simplest way to make a new ISO with just this one file added?

Isomaster

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I would see if package manager has it first. Gonna be a short post as the stitches in my eyeball is still healing and I get headaches looking at computer screen still. Slowly getting better I hope.

Hi, roky. Go easy with your eyes.

Isomaster is in the repos. It opens the iso file and lets one add and remove things. But I don't know how to use it to add a package to the system because the mepis system inside the iso is a compressed file (maybe decompress it and add it to /var/apt/cache or wherever it should be place into).
BTW, MidnightCommander (already in antiX) opens iso files too. I don't know if it permits editing them (but I guess so, by using 'save as').