However, my main question (which may sound dumb) is, “in this scenario would it be better to Refinance the house, or go through with HELOC?”

I’d love to hear what kind of ideas y’all have for the most optimal financing scenario!

For your first one you may want to look into some form of equity position or possibly an owner financed scenario till you get situated down there.

I don't have the energy to play cops & robbers, that's not my job.Separately, as part of management principles, I would always pay attention to patterns, who's the common element in said pattern. 

Duplex tenants would be responsible for landscaping whereas the fourplex will require you to mow the lawn or clean the stairwell and common areas.I would probably take the duplex just because it would attract families with a little more money and probably have fewer complaints of noisy neighbors, parking, etc.

A negative response in naturally the most common response and for the best - it saves you time.2.

Make sure in the contract it allows you to do this, but yes, this is a very common practice.

It is very easy to envision cost overruns and additions to the scope of work here in this scenario. 

My initial hope was to invest in Canada to avoid complicated tax scenarios, but I know members of the BP community have had good success with cross border investing as long as it's structured correctly.I'm looking to work at least 1 more year overseas, but I'd like to start transitioning into investing over the next 12 months if possible to do so from abroad.I'm really excited to enter into this exciting industry, and hopefully work with some of the great real estate minds here on BP!

Don't be scare of slate roofs, they're common and not an issue, just always have a slate guy go and inspect and repair any broken/missing tiles and flashing on day 1.