We use both SolidWorks and Sketchup side by side. Sketchup is our master model, SolidWorks ist for everything that has anything to do with “metal-construction”. We usually predesign in Sketchup so our SolidWorks guys know what we want, that makes the SW construction very quickly. The result is being reimported into Sketchup.
So - I kinda know both ways of thinking. What I love about SolidWorks is that I can pick any part or assembly and make detailed “layout-drawings” of them - complete with part-tables, materials, etc. Since you are used to that, Sketchup will make you cry every so often: “You are done - you can see your part - why is it so hard to get it on paper?!”
On the other hand - it is so much easier to actually design that initial assembly in Sketchup because you don’t have to manage so many files. You just add parts in one file as you go along.
Basically SolidWorks goes from small to large and Sketchup goes from large to small. 
What might help your workflow is the Eneroth Reference-Manager. With that you can sort of simulate a Solid-Works-Like Workflow, because it helps you saving parts and sub-assemblies out into different files and it keeps it all connected. It’s quite a bargain for what it does.
Sketchup will never be anything close to SolidWorks however. Once you get close to production, you will need additional Tools - at least something like AutoCad LT to smooth out those crinkely curves…