Didn't mix priming sugar well enough

I goofed and didn't mix my priming sugar into the beer well enough. I did what I usually do and put the solution into the bottling bucket and then racked the beer onto it. I had a pretty gentle racking for whatever reason, and even though I had a nice, slow whirlpool, I don't think the sugar mixed in very well..

I checked the gravity with the little bit left in the bucket after bottling and it was 10 points up (and tasted really sweet).

It was a small batch, about 2.75 gallons being bottled with 2.4oz of corn sugar. There was probably 10-12 oz of beer left in the bucket when I checked the gravity. If it was 10 points up from the FG checked when I moved it to secondary, how much of my sugar was down in those dregs? My math is coming up with about half an ounce of the 2.4, but that could be way off.

Here's what I am confused about though: if the sugar settled to the bottom (which it should, given the chance) and I filled the bottles from the bottom of the bucket (which I did because that's where the spigot is), wouldn't the most sugar have gone into the first bottles and the remaining solution be *lower* in sugar concentration at the end of the bucket?

At the end of the day, it's done with, so I'll just RDWHAHB and hope it all just works out. But, can anyone help make sense of this for me? I've never measured the gravity of a batch at the very end, after bottling like this, and I don't know what possessed me to do it now, but I think I'm just excited about this batch as it has smelled so good since I brewed it.

I never mix my priming sugar, just place it in the bottom and let the natural movement of the beer as it racks on top of it, mix it up. I tend to believe that you don't need to mix it at all. It's only 2 cups of liquid being dilluted into 5 gallons.....

That's usually what I do. I'm sure everything is fine. I think the excessive amount of chaos in my house today (I have a toddler and an infant), added to these long, cold winter nights are just making me panicky for some reason.

Thanks Revvy!

EDIT: This, thankfully, will be one of the last batches - maybe THE last - I have to bottle and carb. Freezer for the keezer is in the garage, next paycheck has some OT in it to pay for keg parts, and I am sketching out the designes for the coffin/counter top this week...