It appears you consider things in a series of linear events. All considered many investors use leverage, of many forms. Housing being the most common for sure, certainly, you can use this in your application. You'll see the questions asked here about using a HELOC for investing, it's in a sense similar to what I propose.
You've mentioned putting everything on hold for your current debt. That being said, if you were to refinance or already have your debt below your expected return rate of your investments, perhaps it could be better moving money investment way, even if you are paying out on that debt.
In simple illustration, if your debts are 4%, your expected return 7% from investments, it still looks as 3% before fees, inflation, etc. However, even like true margin accounts, you should only leverage just as much as you feel comfortable. I've previously been as high as 23% leveraged before. My comfort isn't really much higher. Many here are zero. Many have houses that change the variable, but appears a different wrapped present. As evidence, take a peak at the forums discussing paying off your mortgage vs investing. It's a heated debate, which uses leverage; but only if the numbers make sense. If you're not plotting to be in the positive, I certainly wouldn't go near it and thus pay off that debt as quickly as possible.
Finally, using the leverage, always have it accessible to be called on. If you can't liquidate your position quickly, to cover the cost loaned to you, also, don't be in that position.