Eeesh. I'm going to be bringing you bad news, I'm afraid.
No. You're stuck. AE just doesn't do that. (I'll share some good news later, but that's the short, simple version.)
The results are the same no matter if I use GPU Acceleration (OpenCL) or Software Only.
This won't make a difference on CPU use. However, GPU acceleration will make a huge difference in speed if you are using GPU-accelerated effects (Glow, Fast Gaussian Blur, Lumetri, etc.)
And the 3D renderer (classic, ray-traced, etc.) shouldn't affect normal rendering of comps with no 3D Layers, right?
Right. What renderer you use only affects the rendering of the 3d geometry/lighting/shadows that are being created by the renderer. All of your normal stuff (Effects, Plugins, etc.) are unaffected.
Side note: if you do use the new native C4D renderer in your timeline, it is a truly multithreaded renderer (for the 3d geometry it creates). It is actually using C4D's renderer under the hood for those parts and C4D will use every bit of processing power you have.
Okay, now for the good(ish) news:
There are third party tools (BG Renderer, for example) that can make your system use more of its power, so you could try that.
Alternatively (and just using the CC subscription you already have) you can Save As version 13, open it in AE CC 2014, and render with multiprocessing. (AE version 13.2 [AKA CC 2014] is the last version of AE to use the old architecture.) Now, this is subject to the bugs and idiosyncrasies that have plagued multiprocessing since its inception (and caused its demise), but it does make a huge difference in some instances. It's not truly multithreaded as it just spins up a bunch of instances of AE in the background. There are some expressions and effects that will disable multiprocessing (check your info panel to see if it says multiprocessing has been disabled), but if all is well, things will go faster (over the course of a longer composition, that is. If it's a fast-rendering thing, sometimes the overhead of launching all of those instances of AE in the background just isn't worth it.)
Further good news:
The AE team is still working on the new architecture in After Effects that was partially introduced in CC 2015. They have said that they are still developing the new renderer. They are looking at all options including CPU multithreading, etc. to make it faster. So please, please, please file a feature request to bring a true, multithreaded renderer to AE! My 16 cores (32 threads) would really, really like to get to work and the more of us that vote, the higher priority it gets!
thanks so much for the quick and detailed reply!
While I won't have the time to try BG Renderer right away, I will file a feature request ASAP. And should I get a chance to try this or another tool, I'll be sure to post back here.
Please do keep us informed!