If you have an angle grinder go to Home Depot or equivilent and buy a concrete cutting disk. The have wheels that look like metal grinding disks but are specifically for masonry. They also have a concrete grinder blade set up which is steel but has what I assume is a diamond filled bars on the bottom. It will last a lot longer. If you don't have an angle grinder go to a rental place and rent the same kind of setup. It will probably be a bigger unit with more power so you will be done faster. You can get a nice finish if you are careful.
I do in fact have an angle grinder and even have a masonry disk. But I've only used it for cutting, not grinding. I'm guessing you use the edge of the disk and move it back and forth. If you used it flat-face it would seem like it would wear the disk too thin.
That's to much for a grinder, put a diamond blade in a skill saw and build a jig so it just hits what you want to remove and 400 passes later, clean it up with grinder, again diamond blade, 2 different blades, a/$100 each.
I did understand your dimensions correctly 6 inches by 6 feet by 1/4" depth? Buy a 4" Ridgid diamond wheel cup, $39.95 at home depot or similiar store and it will take your area down rather quikly. You might be able to rent just the cup but I doubt it. I will include the web site just so you can see what I am talking about.