> IE *x and *hW both merge to Anatolian
> *h while IE *h disappears

Well actually, h3 (your hW) appears to be lost or assimilated medially.
Hitt lahu "pour" must continue *leh2w not *leh3w. Its reflex in initial
position is disputed. Craig Melchert suggests it is lost in Lycian, but
appears as h in Hittite, Palaic and Luwian. He offers as evidence PIE *h3ep
"work" ?> Hitt happar "sale, Lyc epirije "sell".

This doesn't substantially affect your argument about the stickiness of the
hs 1, 2, & 3, however.