Stay with the footage direct from the GoPro.
Open Premiere Elements 12 to the Expert workspace.
Go to File Menu/New/Project and Change Settings.
In the Change Settings area change the project preset to
Before you exit that area, in the final dialog that you see there (new project dialog), make sure to have a check mark next to "Force Selected Project Settings on This Project".
The key thought with the project preset here is to select one that will direct the program to establish a 1280 x 720 project space in the Edit area monitor. This decision is not dependant on frame rate unless you require frame by frame editing which I do not believe you are.
Then back in the Expert workspace, import your video into the project, using the program's Add Media Files and Folders. When you drag the file for the first time to the Timeline, you will get an orange line over the content. That is that program telling you that you need to render the Timeline content to get the best possible preview. It is often a tip off that you are not using the right project preset. Ignore that. It is the 47.952 frame rate that is forcing the program to throw off that render indicator. Rendering the Timeline is for preview purposes only.
What is the quality of what we have up to his point, unrendered or rendered.
There is no 47.952 frame rate for Premiere Elements. Are you in a NTSC or PAL setup?
You may have to take the original into HandBrake or another program before import and change the frame rate to a constant 25, 30, 50, or 60 progressive frames per second.
More on that later.
Please review the comments to this point and then we can decide what next.
Okay. I followed those directions exactly.
Pre-rendering with PE: It doesn't look great on my larger monitor (pixelated/slightly choppy before I render it) it is slightly better on my laptop. Also, the Cineform/GOPro conversion to AVI supposedly removes some of the fisheye effect. I would love for that to work but given the other issue I'm having with the AVI files being truncated from 17 to 3 mins maybe I will just have to deal with the fisheye issue (which is pretty bad with the SuperView setting-I wish I could go back and choose another setting, but I can't) if I can get this resolution issue resolved.
I tried to render it and this is the first time this has happened (not saying much since I am new to this program). The whole screen is bright red. I am going to try and export it and see what happens then. The little preview screen isn't red and it shows it being about the same as pre-rendering. I will report back after it has been exported.