Help cleaning up hardwood cuts

I've got a project to make a jewelry box out of purple heart wood. I've got all the pieces cut to size and the front and backs made into pin boards. I used a table saw and jig to get to this point and the other side of the jig matches for the tails but I set it up to cut just 1/32 shy of my depth line. I hate how the blade leaves that tiny v shape, so I thought I'd take that last bit out by hand.

Now I'm baffled as to how to get that last 1/32 cleaned up. After an hour of using a file I have 4 out of 36 slots cleaned up. This purple heart wood is stupid hard and I'm afraid of getting tear out if I try to use a chisel. Any idea's?

http://farm3.staticflickr.com/2891/8858994832_c441f3b48d_h.jpg

On a hardness scale this stuff seems to rate just under 2000 where Oak is 1400 and dough fir / spruce 650-700.