Henry does not totally ignore the lower lux tax line. He has a long history of re-setting the tax, even when it looked like we might be one or two costly players away from being even more serious contenders.
We stayed under in 2003 and re-set in 2008, stayed under in 2009, reset in 2012, stayed under in 2013 & 2014, reset in 2017 and again in 2020.
Since the 2004-2007 run of paying a lux tax, we have never gone more than 2 years in a row, so yes, he avoids the big 3rd year tax bigtime, but he never even goes slightly over year 3, which wouldn't be a big tax.
I remember that 2012-2014 period, where we went 3 straight years without paying any taxes. Ben's budget was very limited compared to other GMs, but we still managed to win a ring in 2013. Many fans were upset we didn't spend more (and more).