It's a solid and robust model. Ultimately the better approach would be to calibrate the Pars (and recalculate all scores) after every game. I suspect you could probably calculate it on the basis of the home/away for of each team after every round of fixture. That's impractical and would introduce some fairly erratic results early in the season. There is the odd except year on year however the approach is pretty sound and indicative when looking for things like top 4/relegation. I think you've stated previously Prof, you don't consider it a highly predictive measure for individual placings given in the final weeks of the season all manor of intangibles come in to play.
It absolutely works, and I can't wait for week 8 of the season when we can discount that show of b*stards Mourinho has assembled from getting anywhere near the top 4 this year.
I think the full previous season's results will usually provide a more accurate model than what you suggest here. (eg, Watford are currently second.) It would be a pain to produce, and the results would be confusing and contradictory from week to week, with team's points totals yoyoing all over the place. You lose a lot of clarity, and eventually you end up more or less where you began. The par 3 teams tend not to change radically from one season to the next (though they fall in and out of the top half of the table several times over a season.)
Also, worth bearing in mind that the APLT is a model for winning the league, and it's usefulness for teams battling for top four, for example, will be significantly weaker.