In order to be eligible for 1031 treatment you must take deeded title to investment real estate. 

An Opportunity Zone is an economically-distressed community where new investments, under certain conditions, may be eligible for preferential tax treatment.

Right now you've probably got long-term capital gains treatment for your rentals. 

The partnership can certainly sell relinquished property held in the entity’s name and then purchase like-kind replacement property to be held by the same entity and still qualify for 1031 Exchange treatment.

I'm considering a move to a state where there are no income taxes (Washington, Alaska, Nevada, or Florida), and I'm having  hard time determining the tax treatment of the interest income I receive from the Oregon-based mortgage notes. 

The IRS may allow the investor the tax treatment the investor had a reasonable expectation of receiving in light of due diligence.

If your plan is to elect for the LLC to be taxed as a corporation, then you will have no disconnect between the tax treatment in both countries ... and if this LLC is a 100% child subsidiary of a Canadian corporation, you will be able to repatriate retained earnings to the parent corporation with little to no taxation from the CRA.You, and your partner, should spend a little money and sit down with a {Canadian} accountant, and possibly an attorney, experienced in cross-boarder business and determine the best ownership stricture to meet your current and anticipated needs ... before you start shopping.

The only way you could receive long or short term capitol gains treatment would be if you rented them for the required times as stipulated by the IRS.

Granted, I have not at all looked into the tax treatment of such a strategy after having put the money into the DST, but at first glance I see this to be the final move if and when one gets (older and/or) to a point where one no longer wants to deal with being a landlord as an individual but rather a purely passive investor.

Properties that are acquired for rehab/flipping do not qualify for 1031 Exchange treatment.