I like the idea overall, but there are some points one should be aware of.
If you assign the favored and deficient stats pre-roll, that would also seem to mean needing to have stats all pre-assigned too, right? Some players might not go with that.
If instead, I allow them to first roll 4d6 drop lowest or 3d6, then assign, then add the extra dice for favored and deficient and drop highest/lowest accordingly, then I would expect the final results to be skewed more strongly in favor of high scores, as this method can be "gamed". For instance, if one [13] score is the result of [1 6 6] and other is [4 4 5], assigning the first as favored would very likely improve it (chances are 5 out of 6), while assigning the second as favored results in very low expectations (2 out of 6). If one was to pay the favored score by using a [9] stat like [3 3 3], they would feel like a very profitable deal, as the chances of reducing such combination are only 2 in 6, and only 1 in 6 to actually reduce the final modifier.
I'm very confused by this post. You roll all the dice at the same time, just like you would when rolling 4d6. You just roll 1 more or less. If you've rolled 5 dice, you can't then say that wasn't one of your favoured stats. Likewise if you rolled 3d6 when you would normally roll 4d6, that's clearly a deficient stat roll.