Right now the center is 6 x 6 blocks. To keep the same look, both dimensions need to be even, but since you don't want a square quilt, they won't be the same.
The math geek in me and my process:
6x+2(x-1) = width of center. Simplified: 8x - 2 = width of center.
6y +2(y-1) = length of center. Simplified: 8y - 2 = length of center.
The border is currently 5" finished. I'd go up to about 10" if needed.
So to get to about 83" x 96", I do this formula:
8y - 2 + 2b = 96" (length of quilt) (y = # of blocks down, b = total border width)
8x - 2 + 2b = 83" (width of quilt) (x = # of blocks across, b = total border width, assuming same horizontal and vertical border width)
Subtract the two and you get: 8y - 8x = 13"
y - x = 1.625 = equals # of blocks more down than wide. Round up to 2.
So using a 10" border, we get:
8y - 2 + 20 = 96
8y +18 = 96
8y = 78
y = 78/8 or 9.75 blocks down. Round up to 10 blocks. Since we know from the previous formula that we need 2 more blocks down than across, so we need 8 across.
So instead of doing a 6 x 6 layout, we will be doing an 8 x 10 layout.
Now lets calculate the size of the quilt and make sure it meets your needs:
8 * 8 - 2 + 20 = 82"
8 * 10 - 2 + 20 = 98"
82" x 98" is pretty close to 83" x 96". If you absolutely need it to be 83", then increase the border by 1/2" so that you have a 83" x 99" quilt top.
8 x 10 blocks = 80 blocks versus the 36 blocks that you originally needed, so make sure to get more yardage for the blocks AND for the sashing. Of course, you also need to increase the yardage for the borders in both width and length.
Since the original pattern calls for two borders - 1" finished and 4" finished, you can add a 3rd border to get to the 10 1/2" you want. Maybe try a 1", 2", and 7 1/2" or some other similar method.
This works better than the 9 blocks x 11 blocks that someone suggested because it keeps the same layout pattern as the original quilt.
(just a side note ... this is how I use math in everyday life!)