Synthesis of 1-hexene from 1-octyne
On the plus side, you've clearly thought about this problem and have worked out a detailed synthetic route.  I think most of the steps would work as desired.  The two steps that concern me the most are 4 and 7.  I suspect your step 4 will give a mixture of products.  Perhaps with further experimentation you could find reaction conditions that would give you the desired product without  other products from undesired side reaction (elimination in the other direction and perhaps some rearrangement products too).  I see your step 7 as the most problematical.  Aluminum chloride, heat and the alcohol will produce a carbocation and it will undergo significant rearrangement creating a variety of elimination and addition (polymer formation) products.  So while your reaction scheme is plausible, in my opinion it is not efficient.