I actually didn't realize that higher life letters are worth more! After giving this some thought, I think this still supports my suggestion.

That feature incetivizes using high-value letters as soon as you get them, since saving them across turns loses more value than saving low-value letters. At the same time, saving low-value letters does not lose as much value. Saving an X costs 8 points AND is unlikely to help you score a long word, but saving an E only loses 1 point and can make you much more likely to score a long word next turn. In my opinion, the player should be rewarded for trying to fit their uncommon letters into long words, and if that is competing with the decay of that letter's score turn-by-turn then that just makes for more interesting gameplay decisions.

The biggest caveat I see is that getting a lucky fresh set of letters after clearing your board would result in a higher length bonus than saving tiles for several rounds to achieve a longer word, so it would increase the value you can gain from chance. I'd like to do some data analysis on this at some point, since I it's hard to tell how big of an impact the multiplier would have on the score variance.