I'm a civil engineer in the private sector consulting world, but was in the Army and Army Reserve, in the engineer branch the entire 12 years as an officer. I liked most of it, the reason I didn't do 20 is that I got banged up in Afghanistan and medically discharged. Anyway, "Combat Engineer" could mean about a bazillion things from dealing with mines, building fortifications for tanks and artillery, I'm sure you've looked into it. I blasted weapons caches in Astan, taught Romanians how to extract themselves from minefields, built bridges, and also fixed the general's toilet in the reserve HQ stateside. So there is also a fair amount of "hey you" and non-combat engineering when you put on that Army castle. I did as much of that as I did combat engineering, like bridging, horizontal and vertical construction. You may also want to look into those fed jobs for USACE positions. They snatch up lots of people with your background, both as a DOD civilian and/or as a green-suiter, or actual Army officer through direct commission, to work on all types of projects, usually big ones.
I just do airport projects now and generally like it. I also concur with the advise about getting into the contractor's side, whether it's big or little construction. Big, I mean with big facility contractors. Little, I mean residential or commercial developers who need engineer-types to both design their structures where required and also navigate the myriad of local, state, federal code requirements on every project.
Somewhat of a sidebar, if you want to go crazy and do both, like a few years active duty followed by rounding out your 20 in a military reserve, it is infinitely easier to do with some sort of government day job. I say military instead of army reserve because all branches use engineer officers. I worked with Navy, USMC, and USAF engineer officers both stateside and downrange all doing largely the same thing. And switching branches isn't that big of a deal in the first part of your career. Taking off the time needed for reserves in the private sector is much more difficult than if you have a fed, state, or local gov day job. It shouldn't be that way, but it just is. I supposed giant corporate conglomerates of thousands of people could be different, but I bet not much different.
RE: wlm1313 and the CAD projection, I feel your pain. There is a lot of misinformation floating around out there with respect to land surveying vs. instrument operators. Having a healthy knowledge of good info vs. BS in the land survey/coordinate system world is crucial to our projects and I'm frequently frustrated by people with enough knowledge to be dangerous.
Go with your gut. Life is short. From what I see, the job market hasn't been better and doesn't look like it's slowing any time soon. So try something out, if you don't like it, move. Hopping around when you're young doesn't look nearly as bad on a resume as it does when you're long-in-the-tooth like me. All this reminds me I need to get back to an old college buddy who pinged me with a similar question a couple days ago...
Best of luck.