The recommendations for R-values in attics has increased. Since your insulation doesn't come up to the top of the framing I'm guessing where it's not low it only comes up to the top of the framing. That means even if you had the insulation to the top of 2x6 joists you'd be below the new minimum recommendation.
Blowing insulation is usually easier and cheaper than laying batts. You may even find someone to do it for you for less than the cost to buy batts.
If you're going to the trouble I think you might as well consider adding enough insulation to meet the new recommended minimum. Then just add more blown in insulation. You'll save a lot of time compared to sweeping the old and then spending all that time on your knees in an attic cutting and installing batts. Probably save money to and get a more energy efficient attic.
You can rent a blower and I think if you buy a certain number of bags some of the big box stores will include the blower rental for free.
I'm looking into blowing in insulation over my existing batts because it's going to be cheaper than adding an additional layer of rolls.
Update: You didn't indicate the size of your attic or how many square feet you have that needs added insulation.
If you only have a small area to do such that renting a blower is cost prohibitive (less than 10 bags so no free blower rental) or a PITA you can always apply the blown in insulation without a blower. It's easy to break up by hand and sprinkle it over the area then rake it smooth. You can also drop chunks of the insulation into a clean, empty trash can (maybe 5 gallon bucket if you can't get trash can up in attic) and break/fluff it up with a paddle mixer on a drill then pour it out into the area.
Either way I look at it, adding more loose fill seems to save steps, time and money.