If you drop the 4th string, I think you'll find the 105 will be too floppy. I use a 110 and still have to raise my lowest during higher than usual for a setup.We play Higher by Creed. So I have drop down to C#, just like you said. This is why I decided to see if the heavier gauge works well first.
I will probably end up buying a set at 50-70-85-105, just to compare the two.
I typically find when I change strings types, a full setup is necessary.
DR make Drop Down set, with a heavier core. They work pretty well, even just as regular strings. They are stiffer. I hear Jeff Berlin using them in E standard tuning. I have too and like them.
edit: and you'll at least need to adjust the truss rod.