I think you could do the sleeves in the round if you wanted to, but you might want to do it like they say so you don't have to do anymore thinking than you have too.
But if you're up to it, go for it. I went and looked at your little sweater and I'm thinking that the patterns in the sweater are produced by the yarn itself and not color work, is that correct? That makes it that much easier. What GJ said will work if you choose to do a sleeve in the round.
I wanted to speak to the other questions you had about the increase instructions. When it says to increase at the beginning and end or row 3 and each following 4th row 6 times it will mean to increase at each end of row 3, then NOT on rows 4, 5, and 6 but again on row 7 which will be the 4th row after row 3. So every increase row will fall on an odd row. The increases will be on row 3 first, then rows 7, 11, 15, 19, 23, 27. That will be the 6 times. And then it says to increase every following 6th row 4 times. You will want to increase at the beginning and end of the rows still or it would make the sleeve uneven. Those will fall on rows 33, 39, 45, and row 51, again all uneven rows.
You said the way you had it figured out you would be 2 stitches short. Well, if you increased at the beginning and the end those last 4 times you would gain 8 stitches over the course of those 4 increase rows. And the way I outlined for the first part you would produce 7 increases at each end for a total of 14. 14+8= 22.
The way you had it figured was increasing on rows 3, 4, 8, 12, 16, 20, 24, and 28, at each end, for 16 stitches gained, then increasing the last 4 times only at one end, for a total of 4 more. 16+4= 20.
So you see, the way I suggested gives the 22 you are looking for.
It's a cute little sweater. That real fine yarn is why it is taking you so long, but the result will be nice. In the picture of the one on the baby the little sweater looked real short in the sleeves and the body. Maybe they only had one size sweater to choose from for the picture, and one size baby, and they did not match.
IOW maybe the baby is too big for the sweater and that explains it. The 6.5 inches for a 9 month size doesn't seem too bad, but if you have a little more yarn you can always make the sleeves a little longer without it causing any trouble if you want to.
I guess it is okay if the baby comes before the sweater is done, since it is a 9 month size.
You'll make it.