I want to back up system files and installed programs ONLY

See this
https://www.sevenforums.com/backup-restore/43219-image-your-system-free-macrium.html
I recommend it over the Win 7 imaging utility.

Keep in mind a system image is an image of all data on the system partition.
Restoring the image will make everything operate as it did when the image was taken.
That's assuming all programs are installed on the system partition, or haven't been moved from their install locations.
So here's a few tips to keep it simple, and have all programs operate as they did when you took the image.

Install all of your programs on the system partition.
Keep your system partition clean of non-system data, unless you want it included in the system image.
Be aware that some programs will keep data on the system partition.
Sometimes it's important if you haven't backed it up elsewhere.
Quicken is an example, though data may be re-downloaded. I use a PIM where I often enter appointments and such.
I make sure I save that before I restore an image, otherwise it's simply gone.
So make sure that for anything you want, you have saved it elsewhere before you restore an image.
The same applies to My Documents, save game files, etc.
That will all be overwritten by restoring a system image.

The registry is included in the image. Don't worry about it.
Just be aware that it contains pointers to program locations.
So any program using the registry (most do, but not all) installed after the image was taken will have to be reinstalled if you restore the image.

Thing is, I don't have a reliable external drive to contain a mass data transfer to make room for a data partition. My first time around installing Windows to my 128 GB SSD I was either in too much of a rush to do some things like partitioning, or I just plain forgot. As it stands, I have ~31 GB of stuff I want to back up, and ~72 GB of "other". I want to keep the "other", but in case of an emergency crash I'd rather lose those things than do a completely fresh install.

I'm trying to avoid mass data transfer in general, because at that point I might as well just create an entire system image and spend more dollars on an external drive, which I'm also trying to avoid. I can allocate ~31 GB of "other" to my iPod temporarily to make room for a dedicated OS partition, back up the stuff I want, unpack or whatever, switch the boot partition, and delete the redundant stuff from the data partition.

I know all of that just fine. But that seems much more time-consuming and labor-intensive than just backing up the stuff I want to my iPod and then to my friend's 4+ TB desktop setup. I want to do quick backups for now, and then do that whole mess later when I have time and money to spare.

Hello MindNarrative and welcome to Seven Forums

There are some 3rd party backup imaging programs that allow excluding specific files to be included in the backup image.
It sounds like that is a feature/option you want.
I use Acronis (PAID), and can exclude files, so I can exclude "C\Users\*.*" from the backup image.
The free version of Acronis available to WD or Seagate HD owners does not have this option/feature.

Are you willing to pay for a Backup Imaging program for this feature?

There are many highly recommended imaging programs available, free versions and paid versions (with a free trial).
Maybe someone here knows of a free program that can do what you want, I don't.
If not, you can try various imaging programs and find what works best for you.

I too want to exclude certain files from the backup image such as pagefile, hibernate file, temp files, etc.
So for me, paying for this feature is worth the cost to reduce image file size (and time needed to create the image).
I store my User Data on a different partition using Libraries, so I'm not concerned with space used for the "C\Users" data...

Hope this helps,
David

Given what you've said, my alternative to imaging would be to set up system restore.
Don't use it myself, but I'm sure others here have had success with it and can advise you.