Insulation, Radiant and Vapor Barriers - adding insulation

We just bought a raised ranch in eastern connecticut. The attic is poorly insulated, about 2 to 3 inches of fiberglass batting. We want to add unfaced on top of this.
I have read posts where you recommend adding batting up to the top of the joists then more batts perpendicular to the joists to stop heat loss thru the wood joists. How can I criss cross the batts and still have a rough floor in the attic for storage? Do I have to put 2x4 or 2x6 criss crossing the joists, then put subfloor in top of these? Are there any DIY alternatives to batting which will give me more r factor per inch, like foam plank that fits down in between the joists. I visit many forums on the do-it-yourself website and think that all of advice provided is great. Keep in up.

If you want a high R on the insuation you want about 12" or more. So there is no way to do this unless you raise the floor that you want.To buy the foam panels like you say and use them the cost for them would be just to high for the R you get from them. Add the 2x6 across the joist there now and fill in with batts no paper you can go 24" on center for them and home depot hads a 5/8 ply just for this in T/G for the attic floor ED;)