With all this said, I’m really trying to convince my wife to do a multi-family house hack as this would jump start a truly amazing compound effect without having to purchase a forth rental for a while.

Would you all recommend this route or know of any better ways to compound my savings?

We bow to your every word, and you can never be wrong. 

@Joe Villeneuve I bowed out and decided to step away from the opportunity...

If you're young these are important years to build a retirement fund and start the compounding interest earning you more money on what you already have.

I believe that the key to successfully running properties rented by low-income tenants is being willing to solve problems for people that the lease doesn't actually require you to solve but that your tenants will probably be unable to solve on their own; sometimes you must bow to reality regardless of what you are entitled to under the terms of the lease.

Stay the course and your efforts will continue to compound over time.House hacking is a fantastic way to get started since it's low down real estate investing and you build your landlord experience while also meeting your own housing needs.

Compounding is definitely on your side. 

They are not bowed out or seem to be on the verge of collapse.

Inspection revealed major issues with the property, some of which were not disclosed: evidence of foundation problem (stair-step and horizontal cracks, bowing towards the inside of the basement, uneven floors in units); basement leaks, roof leaks, 1 furnace is putting out carbon monoxide and needs to be repaired, etc.