MG:
You and I are the same age. Actually we followed parallel paths for a while, as I had a 3 year diploma (similar to a technology degree here in Canada), went back to University ~11 years ago, got an engineering degree from a well ranked university, then went out into the working world.
I spent a few years doing design but mostly drafting for a company building industrial machinery, so I had the opportunity to crank out many drawings, and experience many issues on the shop floor due to mistakes (mine and others). Do I love drafting? No. But I've experienced enough of the aforementioned issues to know that simple little mistakes in the drafting process have the potential to throw months of effort and millions of dollars of investment down the tube. So I recognized it was important and when I had a stack of drawings to create / review / approve, I took a deep breath and dove in. As some had also experienced, after a few years of it I managed to propose ideas both for designs as well as process improvements that served the company well. Felt good when it happened, but the drafting work never went away.
About 2 years ago I was contacted by my current employer, who at the time was just a small but growing startup of about 40 people. I joined as a mechanical engineer, and have had the chance to work on some pretty cool stuff. We're in the medical device industry, and our products include optical systems, robotics and medical imaging systems. Sometimes walking through the R&D section feels like walking through Q-Branch in a Bond movie... but guess what? I spend a huge chunk of my time doing... yes... drafting, not to mention procurement, shipping, receiving, building, testing and Change Order-ing (all "grunt work" as you called it). Today my title is Mechanical Engineering Manager, but I like the title "guy with the dirty hands" instead.
I had ZERO experience in medical device design when I joined here, but I had extensive drafting and design experience. In fact, based on my previous experiences as a drafter, I've had the opportunity to write our company's internal design and drafting standards from scratch. As my team grows (company has quadrupled in size since I started) I get to do less of the drafting work, but I will never fully give it up as I have taken ownership over the quality of our company's outgoing drawings.
I guess the point of all of this is to say that the grass is only as green as you are willing to recognize it to be. I would not have been able to do what I'm doing today if I had the attitude that I hated what I was doing. When I was approached about this job, it was made clear that they needed someone who could do much of the company's mechanical drafting as we grew. If I hated drafting, I would not have made the jump to (what was at the time) a high risk startup. Sure, I'd love to be spending all of my days coming up with cool concept designs for the next MRI-guided surgical robot. I know that days like that are in fact on the horizon, but we as a company won't get there tomorrow unless my team and I knock off the pile of drawings on our Next-Actions list today. And once we do come up with that awesome concept, it's going to mean another pile of drawings in our N-A list. We need to take the bitter with the sweet.
But, if you carry this hatred toward your work that you seem to espouse, and want to "get into a mid sized company with a support staff so (you don't) have to do all the grunt work" then its not that likely that you're going to get to do anything truly great. Your choice.
