I do not have a large down payment saved up but I have been considering making a large withdrawal from my 401k, about 35k worth.

You want to invest just to have a place to live and potentially offsetting your mortgage payment by renting out the vacated rooms or having x amount of cashflow in the future?

I highly recommend managing them yourself, at least the bill paying, tenant screening, rent collecting aspects, and finding reliable plumbers and heating/cooling people- these are the services you'll use the most. 

Do you have to start making payments right away when you close or do they give you time to get the construction complete?

Otherwise it feels a little sketchy to me, and I would not risk having to evict them after only three months payment.

My current W-2 income will probably not be enough to qualify for the loan, but my income from my current property, which has existed for far less than the two years lenders will look for, gives me more than enough money to be able to handle the payments on such a loan, if I could qualify. 

What is the best way to go about pulling from the $100k in equity in the first property for a down payment on the next property?

Remember that principal payment is not a cost, but you eventually include depreciation.

My point, however inartfully stated, was the underlying payment obligation needs to exist to put others on notice. 

A lot of people will tell you, and they are right, when you do a small down payment, finance, and str the house you should be happy to break even and have a vacation house that someone is paying for you.