I just the Jordan video too....the weight really makes a difference along with a non slip ruler.

Great advice. I learned to walk the ruler with my left hand - I'm right-handed. This is important as well as standing up when you cut and being above the fabric...not trying to cut from an angle. Maybe you ARE trying too hard. That shows you want to do a good job. :) Straightening your fabric several times isn't unusual for a really good straight cut. Zipping through cutting your fabric isn't smart. Slow down and enjoy the process even if it isn't your favorite part.

I was watching a video and the lady cutting used what looked like maybe a 5 pound dumbbell on the ruler furthest from you; kept the ruler in place. You might try that.

Go on YouTube and watch Donna Jordan (Jordan Fabrics). She is great at giving clear concise directions on how to piece a quilt, but the thing I want you to see is.....she uses a 5# weight on the end of the ruler to stop it from slipping. I have 2# weights and tried it. It works great!! Give it a try, but the videos/tutorials are good too. :-). Ellen

The June Taylor shape cuter works for me but still have to square up after a few cuts.

This for me too, including the trimming a bit now and then to keep the edge square. One thing I recently learned when watching videos about my new Martelli ergonomic cutter is that you should cut straight from your side rather than reaching across your body. I'm working on mastering this. Cutting across your body automatically tilts the roller blade so you are not pressing straight ahead but on an angle. I'm practicing taking a step to the side as I work my way down the fabric, so I am pushing forward with the roller and not tipping it. It really does make a difference, and is easier on my arm too!!!

I've been told that it is necessary to 'straighten' the cut edge of the fabric you are rotary cutting after 3 strips have been cut. So, unfortunately, we all have the 'remaining fabric not straight after cutting' problem. :)

What has produced the best results for me is spraying the back of the ruler with spray baste, then rub a lot of it off. It must be a bit tacky when you're done rubbing it off the back of the ruler. The spray baste makes the ruler stick to the fabric better, so there is much less shifting. The spray baste glue wears off, over time, but when it does, just repeat the process.

Another thing that I do that really helps me cut straighter strips is to press a sharp crease at the WOF fold. It reduces 'elbowing' significantly!

Glad you had success with folding it into 4 layers. Definitely the shorter "reach" helps.
And certainly not trying to work with more than a yard width at one time.
Sharp blade keeps you from the temptation of pushing too hard.
My June Tailor ruler is my go-to for cutting several strips from yardage.

I always struggled with getting things cut perfectly(or even ok for that matter) but the game changer for me wasn't a different ruler it was a craftsy class that offered a different cutting method. If you have a chance I would suggest Debbie Caffrey's Cut to it class, It made a huge difference for me.