You might be able to fly it past a DM, but it requires a lot of finagling. I'll try to cover things point by point.
1. Lesser Tiefling is a good idea for this sort of thing. I wish outsiders could become undead through some other method than Lichfiend. (At least that's the only one I'm aware of.)
2. Why Magic in the Blood? For fun?
Now, the first line under the
Half-Fiend SS Progression complicates things.
"A tiefling is born tainted by evil and saddled with a +1 level adjustment. Tieflings who wish to become half-fiends can do so in just three levels instead of the normal four that the standard template class requires. "
The tiefling this progression works for is defined as having a +1 level adjustment. That could either force a +1 LA on you for being a tiefling and following the rules of this progression or disqualify you from it.
A problem is also created for ignoring the internal consistency of the Savage Species Progression system. That web enhancement already has a version of a Lesser Tiefling. It's a +0 LA Tiefling who is still an outsider. It also has a level that turns it into a full +1 LA Teifling. There may not be a RAW rule out there anywhere that says you can ignore the internal consistency of systems, but there likely should be. Mixing and matching systems is one thing, ignoring the internal consistency of one you use is another.
If you make any argument against that, it should be that since the PGtF states that, "If you use these lesser racial versions in your campaign, you should u se t hem across t he board... Thus, a party that includes a lesser drow should never encounter drow from the Monster Manual in your game." You could therefore assert that a Lesser Tiefling is a normal Tiefling, yet should be able to take the SS Progression for the Tiefling and then the Half-Fiend anyway. That would be somewhat stranger, but would negate the problem of the original statement that a Tiefling has a +1 LA.
As far as the human thing goes, a Tiefling would gain the acquired template of Half-Fiend over its lifetime. It would still be a Tiefling, just one that has more fiend in it than before. It wouldn't suddenly become human.
The entire idea of grabbing a +1 LA, buy it off, then repeat is an interesting idea. You could do it, although a DM would likely throw stuff at you.
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Well, that's my 2 cents. Hope this works well in a build if you have a game to use it in.