In your situation (due to the fact that you anticipate having no debt, or need for it by the time your current residence becomes a rental) a lot of the typical advice - ie cash damming, or undertaking the smith manoeuvre isn't beneficial, or reducing your current mortgage payments (paying interest solely for tax planning/minimization purposes is never beneficial).
However you're forgetting CCA (amortization expense) on the property which you can take (4% of net book value (NBV)) to reduce your taxable income. In your situation (and in most siuations) I'd recommend you take the deduction, which will reduce the taxable rental income. (Note you'll have to allocate some of the value of the property to land which can not be amortized.)
Also when you do convert your home to a rental property you'll want to get a reasonable assessment of the property's fair market value as your capital gains exemption for the old property is only until it's change in use (deemed disposition). Any capital gains from that date forward are taxable. (You should likely talk to an Accountant or CRA, to find out exactly what documentation you will need)
Also if you want to look further into tax minimization (from a Canadian perspective) on your rentals I'd suggest checking out/posting to
http://canadianmoneyforum.com/forumdisplay.php/5-Real-Estate as well.
In regards to your statement:
"Canadian tax law says that if I refinance the city house after it is paid off in order to access the equity to invest elsewhere, the mortgage interest would no longer be tax deductible since I would essentially be using that mortgage to invest for personal gain. Someone please correct me if I am wrong here, I am by no means a tax expert."
Canadian tax law would look to see what the proceeds of that loan were used for to determine its tax deductibility. For example many Canadian undertake what is called The Smith Manoeuvre which is where you pay down your principal mortgage (not tax deductible) and then borrow via a HELOC to invest in stocks. The interest on the HELOC is considered tax deductible (against investment income) as its invested to earn investment income via the stocks. If you were to borrow against your rental house to build your new personal residence, then you are correct the interest would not be tax deductible.
Frugal Trader @ MDJ has dozens of posts dedicated to the Smith Manoeuvre at
http://www.milliondollarjourney.com/the-smith-manoeuvre-resource.htm That Id highly recommend reading (and then talking to an accountant before undertaking it)
Hope this helps, I didn't want to get into specifics as it seemed like you were looking for a more overall strategy/idea of options that are out there - if you want more specifics, post your details and I can try to provide an opinion.