Hi! I use that template all the time, since it's not, in fact, a template at all but the UV Map for the Linden hair. There's nothing else that we
can use. But yeah, that one is the worst of the lot, for a whole bunch of reasons.
And no, if you have anything on the back fringe at all, you can't get rid of the line at the back. The same thing with the front fringe and the line at the front.
The problem is that the map is made so that the back fringe overlaps the main hair piece. It is impossible not to have anything at all on the back fringe, unless you make a good bit of the back of the hair transparent as well.
Let me show you what I mean.
This hair has an alpha that exactly follows the outside line of the UVs on the main hair piece. That means that about a third of the back fringe also has texture on it, as you can see from looking at the UVs. There is a small, but visible, line where the fringe extends through the hair, and you can see it.
For this one, I made an alpha with a totally transparent fringe, which means that it also has a large section of transparency on the back of the hair. This makes the hair look hollow, which most people would find unpleasant (I think,) and it still doesn't completely eliminate that line.
So, as far as I can tell, those lines are one of the things that we are just stuck with, until the Lindens change the Avatars so that the Fringe is withdrawn completely into the hair at the lowest slider setting.
The good news is, it will only be seen at very close range; and most people never notice it at all. It's even less noticable with darker hair colors.
Anyway, if you want a template without the extended fringes, here it is. Just paste this into the Alpha channel. (If you're using a 1024 texture, enlarge it first, or don't paste it in until after you've made the texture 512 for uploading.)
Sorry I can't give you better news!