I have two crash reports for you. The first is with Quantum Storage installed. I thought it might have been the culprit but I still crashed with it removed so the second crash report is without Quantum Storage installed. All other mods stayed the same. No crashes since removing Refined Storage.

Report 1:
https://gist.github.com/Dragnier/65eeddc17ffbd4f242c9883e069683f8

Report 2:
https://gist.github.com/Dragnier/01a089e6787f084d6fb15fe61832145e

Some other mod in your modpack is interfering with the RF API and is possibly having a bad version of it installed.

Thanks for letting me know.