If you have an entity with an EIN, and that entity either owns the property (named on title) or constructively owns the rental, then use that.Otherwise, then SSN.Ultimately this has very little effect on the tax return, liability, etc.

Only interested in STR due to tax benefits unfortunately. 

I don't want to have to open another LLC and file taxes in another state for business. 

Everything has gone up in the last few years around this home.2nd house is $900 (property taxes increase yearly) now.

You get some negligibly protections in an LLC too, and possibly tax.

Are there any tax implications or mortgage barriers to building a home under the "second home" plan and then converting it to an investment property shortly after its finished?

Underwrite allowances for - Vacancy, Prop Taxes, Insurance, Utilities, Repairs & Maintenance, a Reserve Account, and Property Management. 

I am eligible for a $156.00 a day stipend if I travel >50 miles away from my tax home.

Depreciation for tax purposesThe amount of annual depreciation OVERLY offset my net income on the property.

You'll want to make sure you understand the K1/tax filing implications because if you own very small piece of let's say 10 properties in 10 different states you would potentially receive 10 K1s (one for each deal) and 'may' have tax filing requirements in 10 states.