I'm fairly confident in my answers for steps 1-3, but I am not certain how to have the methyl group bonded that is bonded to the alkene carbon leave in step 5 without forming methanol.

Here is what I have worked out so far.

I'm fairly confident in my answers for steps 1-3, but I am not certain how to have the methyl group bonded that is bonded to the alkene carbon leave in step 5 without forming methanol.

Here is what I have worked out so far.

Your issue is hardly with the Wittig reaction, although one could very well nitpick. The addition of phosphonium ylid to carbonyl is generally thought to be concerted: see Which is the currently accepted mechanism of a Wittig reaction? for more details.
From what I can tell, you are having more trouble with the acidic hydrolysis of an enol ether to an aldehyde. As has been pointed out by some comments, your proposed mechanism is not really possible. Vinyl $\mathrm{sp^2}$ cations are very unstable and an $\mathrm{S_N1}$-type dissociation of MeOH is very unlikely.1
Instead, you need to use the fact that an enol ether is very much like an enol. It is nucleophilic on the α-carbon, and you can protonate it on that carbon, almost like you are tautomerising an enol back to a ketone. You could also protonate it on oxygen, but that is an unproductive route: nothing really happens apart from the proton just falling off again.
The oxonium ion thus formed is electrophilic, and water can attack it leading to a hemiacetal.
From here on it is standard carbonyl chemistry.
I have deliberately left some stuff quite vague here.
(1) Just for interest, $\mathrm{S_N1}$-type chemistry leading to vinyl cations has been done before, but with much better leaving groups than MeOH. See: Okuyama, T.; Takino, T.; Sueda, T.; Ochiai, M. J. Am. Chem. Soc. 1995, 117 (12), 3360–3367. DOI: 10.1021/ja00117a006.