I have to disagree with the notion of resorting to DME. You know what results you expect from your brewing process and you should not simply count on course correction through significant additions of dry malt extract. Your goal is to figure out what exactly it is that you expect from your brewing process and gradually hone in on the steps required to achieve that end result. Introducing a DME dependency now will add another variable to account for, thereby decreasing your consistency (At least this is one philosophy. I like to call it THE RIGHT ONE

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I personally despise the idea of gravity-correction using ingredients that are not otherwise included in my recipe. You are an all-grain brewer; you use DME for yeast starters and (maybe) bottling. You obviously have an existing desire to calibrate your process to make this happen. Good for you!
What you have now is a great opportunity to correct your brewing process in a significant, permanent way in order to achieve the consistency AND efficiency you want. If you are hell bent on fly sparging, you will need to play around with some brewing variables to make things happen.
While my gut reaction was to second the votes for batch sparging and consistency over efficiency, you are obviously going to keep fly sparging now that you have the equipment to do so. That being the case, you will need do more reading on the subject. Try consulting some more verified sources than the conflicting opinions often offered on HBT. Read something with a glossary, footnotes, and (better yet) citations. I would recommend Brewing Better Beer by Strong.
Some practical knowledge for fly sparging provided by Strong:
- Closely monitor and adjust pH of brewing liquor (sparge water) to match that of your mash
- Closely monitor and adjust the temperature of your brewing liquor
- Sparge slowly; allow 30-60 minutes for fly sparging.
- Avoid "channeling" (sparge water not rinsing all grains) by gently "cutting" a grid into your grain bed with the mash paddle.
I do, however, agree with the suggestion to crush your own grain. If you want consistency, you need to control as many elements as you can. Personally crushing your own grains is, perhaps, one of the most fundamental changes you can make in the handling of your raw ingredients, short of becoming a maltster. I have improved my brewhouse efficiency by almost 10% by crushing my own grain.
I'm sure you've been given a lot to consider. Weigh each piece of advice according to your personal brewing philosophy and, most importantly, your expectations for the final product.