Hi dlspinks.
Using Terminal would require knowing the name and file path of any large files you want to get rid of to make space for the OS install while reinstalling from Internet Recovery would mean erasing the drive and losing all of your data. There is another way that just requires an external hard drive that is empty or can be erased.
What you would do would be to create a clean installation of macOS on the external drive and then boot using that rather than the Mac's internal drive. Once booted using the external, you should be able to access the internal drive via Finder, delete the large files that need to go, back up the Mac and start the install process for Catalina over on the internal drive. You'll want an external drive that is larger than the internal drive in your Mac by at least 50GB. If this were happening to me, I would partition that drive into two parts: The first 50 GB portion for the macOS install and the rest of it held in reserve for a Time Machine backup.
Here are the steps for installing macOS to the external drive.
1) Connect an external drive to the Mac.
2) Startup using macOS Recovery.
3) Select Disk Utility and click Continue.
4) Select View menu > Show All Devices.
5) Select the volume that appears under the external drive, and click the Unmount button on the toolbar. If the external drive contains multiple volumes, repeat this step for each remaining volume, until they are all unmounted (volume name will appear in gray when unmounted).
6) Select the external drive (above the unmounted volume).
7) Click the Erase button on the toolbar, or select Edit menu > Erase…
8) Type "Testing" into the Name field.
9) Select APFS from the Format pop-up menu.
10) Select GUID Partition Map from the Scheme pop-up menu.
11) Click Erase.
12) Quit Disk Utility
13) Select Reinstall macOS and click Continue. Follow the on-screen instructions to install macOS, but select the "Testing" volume when asked which disk to install macOS on.
14) During Setup Assistant, skip the step of signing in with an Apple ID, and create a new user named "Test". Don't migrate any users from a backup or the other startup disk.
Once you are booted to the external drive, find the Catalina installer which should be in the Applications folder and delete it. At this point you can also cull other large files you don't need from the Mac so that you do have space for the install. Once you've gotten rid of the files you are clearing out, make sure to empty the Trash.
Once you've done all that, boot to Recovery again and choose Reinstall macOS but this time, install in on the Mac's internal drive.
Cheers.