Actually Fallahn helped me with a little shader, and it looks like scrolling the texture in OpenGL
still had issues. Extremely odd. It definitely performed better in more cases, but still wasn't stopping the jittering.
Overall, what I found was that certain video mode settings helped. For example, restricting the window to v-sync while in fullscreen mode stopped the jittering. And setting the framerate to that of my monitor while in windowed helped as well. The best performance was achieved in fullscreen v-sync with no noticeable jittering after playing around in it for quite some time. Disabling threaded optimization was also a necessity to entirely preventing this skipping for me. Note that this was all after interpolation was added as well, as without it, I did notice that the jittering would happen.
Hope this helps anyone who comes across this issue in the future. In the end I was still able to go with SFML, and I highly recommend it. Some of the best documentation, cleanest code, and most helpful forums I've seen out there.
Update: 10/27/2018
An update many months in advance for anybody who comes across this issue in the future, this video here was very helpful:
To summarize, it looks like this is just a problem with dual monitor setups where the refresh rate is greater than 60 hz in Windows 10 (or Windows 7 with Aero). As I've gotten further into my engine, I decided to spend some time researching this topic in hopes that I would find a solution, but I have not. Fullscreen definitely seems to lessen the issue significantly, and sometimes the disabling multi-threading as mentioned in here helped as well. But completely getting rid of the jittering doesn't seem to be possible in this kind of setup. Still works perfectly fine on my laptop @ 60 hz though.