In setting up a large meeting from my computer, I also invited myself. Now
it shows up on my computer as it would if someone else set up the meeting. I
am unable to make any changes but am still shown as the organizer. Is there
any way to fix this without just creating a new meeting?

Forward it to yourself as an attachment. Then download the ICAL file to your computer only (save it somewhere). Now you should open it in a basic text editor, and remove yourself from the recipients list by searching for your email\username. Leave the organizer info intact. Save, delete the other event from your calendar, then upload the new one and send it again to update everybody.
If you are the organizer, you are not a recipient of a request unless it is to a SEPARATE EMAIL ACCOUNT. Make sure you do not accidentally send it to yourself again.