Got any ideas how I can have more space to work with here?
Attach a powered USB hub with a thumb drive maybe? This way I can use some USB devices and have some storage space?
The "best bet" would be to craft your own images, as the WNDR3700v1 is an 8 MB device with a very old SoC (from 2007, 802.11n is from 2009, as just one example of "how old"). Though not quite as tight as a 4/32 device, 64 MB of RAM may be an issue with more than basic packages. See https://openwrt.org/supported_devices/openwrt_on_432_devices for information on how to build/assemble your own images.
The other option is "extroot" which can be a challenge to manage on any device. Especially with an old SoC like the AR7161, you may run into USB performance issues.
Do you happen to know if there is any older images of OpenWRT or LEDE that would fit on the router? If it has only 8/64MB, then why does it say that it can run OpenWRT 18.06.5?
Since it's behind a my main ASUS router with constand firmware updates (and a good firewall), I don't really care about how secure the WNDR3700 is.
The WNDR3700v1 can certainly run OpenWrt 18.06.5. You just can't load it up with a bunch of large packages between running out of flash and risking RAM exhaustion.
Anything older than 18.06.5 shouldn't be used anywhere. There are known, significant security vulnerabilities in 18.06.4 and prior that don't require "outside" attack to exploit. Certainly anything that hasn't had the various 802.11 security flaws patched shouldn't ever have wireless enabled.
Edit: Clean up typos
I followed the extroot option 
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