What do you think about making the tosylate and then reacting with sodium iodide in acetone or acetonitrile. This could work as well and be most reactive.
many ways will lead to Rome...
and yes, you could prepare an alkyliodide this way from your initial alcohol.
just so, I don't see the advantage over PΦ
3 / CBr
4 and thatlike in this case.
btw., with respect to your acetylene-alkylation: If you were planing to work with Na/NH
3 anyway, why not use NaNH
2 to deprotonate your acetylene and have a simple SN-reaction for alkylation?
as a side benefit, you won't need the HMPT ( a solvent I always tried to avoid, even in paper chemistry)
regards
Ingo