Honestly, I think your math isn't matching. Where are you getting $4600 a month to solely pay down debts?

The house debt is good debt and as you build equity, receive tax incentives, and increase your principle there is no reason to lump it in with revolving debt, such as credit cards. Student loans (unless private) also have a tax benefit. It's wise to work out all the math on tax incentives as well as deductions in order to decided what to tackle next. Velocity of money works for debt just the same as it does for investments or savings.

If you want to get out of debt sooner, debt avalanche is the way.