Implausible gravity reading on both hydrometer and refractometer

I just brewed a partial mash version of BierMuncher's Black Perl Porter. This was my second time brewing this beer; the first time went perfectly. This time, however, I'm getting some ridiculous gravity readings for the OG, and I just wanted to check with you guys that they couldn't possibly be right...

The gravity-contributing ingredients are (5 gal batch):
- 1.0 lb 2-row
- 2.0 lbs Munich
- 1.0 lb Caramel 20L
- 1.0 lb Chocolate
- 1.0 lb Flake oats
- 4.17 lbs Extra light DME (boiled 10 min)
- 8 oz Malto-Dextrine (boiled 20 min)
- 4 oz Lactose (boiled 15 min)

My target gravity was 1.074.

All of the grains were mashed using DeathBrewer's stove-top method. At the start of the boil I had 3.875 gallons of wort at 1.047 (~11.75% brix), which makes 182 gravity-gallons (a.k.a. "total gravity units" in Ray Daniels' Designing Beer book). My target of 5 gal at 1.074 was 370 gravity-gallons. So my deficit was 188 gravity-gallons, which at roughly 1.045 gravity per pound of DME per gallon of water implied I should add 4.17 lbs of DME during the boil in order to achieve my target gravity (my original recipe called for 4 lbs, so I was only slightly off).

I realize now, that when I did this calculation, I totally forgot to account for the gravity that would be contributed by the 12 combined ounces of malto-dextrine and lactose, which I hadn't yet added. So I should expect my OG to be higher than the 1.074 target, but not by a whole lot, right?

Well, after topping off to 5 gallons and aerating thoroughly, I drew my sample of wort and read its gravity first on the refractometer: 24.75% brix! This works out to about 1.110! I was like WTF, so I double checked with a hydrometer, and it confirmed, about 1.105 to 1.110 specific gravity.

Is it just me, or shouldn't it be physically impossible to achieve a gravity that high with the ingredients I added, no matter how great my efficiency was? There is not much hops in this recipe (1.5 oz), and in any case, I strained almost all of the hop trub out. What other kinds of factors/errors could lead to such crazy gravity readings? Is there a proper way to take a gravity reading that I'm possibly not following, which could lead to this?

Yup, you're right, the ingredients you listed can't possibly add up to 1.110. Since you confirmed your refractometer reading with a hydrometer, my guess would be you mis-weighed one or more of the ingredients. Maybe a mix-up with the tare function?

Could also be that the high gravity wort and top-off water weren't completely mixed, and the sample you took was mostly wort. It's much harder to thoroughly incorporate top-off water than it seems, and often takes several minutes of vigorous stirring.

Either the stuff was extremely off in weight or the stuff didn't mix right.

Even at 100% efficiency the recipe can't be above 1.085 at 5 gallons. Now cut it down to 4 gallons (no top off water) and you could theoretically be close at 100% efficiency.

Thanks for the replies, guys. It's pretty unlikely that I mis-measured the ingredients, just because of the way they were packaged -- even if I had screwed up the tare function, I couldn't have been off by much, because I know how many bags I used.

So the unmixed top-off water theory seems more likely, though that also surprises me. I would never have guessed it would be so hard to mix! This batch I happened to make a real point of aerating vigorously. I shook the carboy around until my arms couldn't take it anymore, and then my buddy shook it until his arms couldn't take it (kind of a contest ). Would you guys recommend actually stirring the post-top-off wort with a stick of some sort?

I've always just added my top-off water by pouring it through a funnel on top of the strong wort. Maybe I should try racking the water in through a tube that runs to the bottom of the wort, to ensure better mixing?

Edit: BTW, the airlock is bubbling quite furiously, and there's a nice krausen, so whatever happened the yeast (Safale S-04) don't seem to mind