If you did it right, and refinanced out but still own the asset, that's the ideal situation, but finding opportunity to do that today is something "ordinary" investors are really struggling to do, if they're able to do it at all.

The article mentions taxes gained and lost - is this the place to factor in taxes paid on the income from the property (is that taxed at a rate of ordinary income?)

It's not cap gains, flipping is ordinary income tax.

As a result our flip projects will be recognized as ordinary income. 

And it's not cap gains, it's ordinary income, subject o SS/med also.

If I log the requisite 750 hours of real estate-related work a year and claim to be a professional investor, can I use my tax deductions from real estate to offset my spouse's ordinary income?  

@Derek LodaAre you fixing and flipping which will create ordinary income or are you rehabbing and renting?

I cant see why it seems out of the ordinary for a landlord to continue business as usual when the sale was based on a verbal contract. 

The proper tax treatment is to add your net rental income to your other ordinary income, then compute your taxes.  

Since you are generating "short term" or ordinary income, an S-Corp may be a good fit for your business.