What can I do if I cancel IFR when I shouldn't have? Standard procedure for T-38 training is to cancel IFR in the MOA and fly back to the base VFR.  

A couple days ago I canceled in the MOA out of habit and instantly realized that I was above a broken layer between my and the base.

Luckily the other side of the MOA was clear, and I used the extra distance for a more shallow descent than I'd have otherwise done.  

But it got me thinking, could I have asked ATC to get me back on my previous clearance?  Being a military training flight, and military controllers I'm sure they would have been super chill and helped me out regardless.  But in the civilian world what would be the best way to handle this situation (other than "don't cancel IFR")?
Since you used the term MOA, I assume you're in the US.

Within the FAA ATC software (not sure about DOD's), the only data difference between IFR and VFR Flight Following is the flight plan altitude. For instance, IFR might have a filed altitude of "060" (6000ft) while VFR FF might have a "filed" altitude of "VFR/065" (6500ft). When you cancel IFR, the controller amends your altitude and leaves the rest of the data unchanged. They don't actually delete your flight plan unless you cancel radar service. Therefore, to resume IFR, all they have to do is amend your altitude again.

Obviously, IFR and VFR are very different procedurally. When you canceled IFR, your existing clearance was invalidated, so you'll need to get a new one. However, since they should still have all your previous data available, it'll probably be similar. But it's less work for them than a normal pop-up IFR.