You'll still end up with a somewhat smaller sweater than the SnB small size. Here's how you can do the math:
10 stitches divided by 4" = 2.5 stitches per inch
A 48 stitch cast on divided by 2.5 stitches = a 19.2" piece of fabric
A 58 stich cast on divided by 2.5 stitches = a 23.2" piece of fabric
You can calculate the row length measurements in the same way (14 stitches divided by...).
Now, 10 stitches divided by 3" (what you got with smaller needles) = 3.33 stitches per inch
A 48 stitch cast on divided by 3.33 stitches = a 14.5" piece of fabric
A 58 stich cast on divided by 3.33 stitches = a 17.6" piece of fabric
Those are sizes that would only fit a really small person (assuming you were doubling the measurement for a front + back, so you would have a 29" garment circumference or a 35.2" garment circumference). If you're that small, you might get away with making the extra large on small needles. You should calculate the armhole circumference, though, as well, and make sure it's big enough for you.
Otherwise, you would either need to use a size of needle that gives you the right fabric size, or you can recalculate the pattern based on the needle size you prefer.
PS - I'm not sure I qualify as a super-experienced knitter, but I like math!