In my experience, underwriting single family home rentals in California typically results in sub-4% unleveraged returns, which is awful given the alternatives. 

Yes, they should be happy to do it and yes, you'll have to find alternative solutions for the buy and rehab.

Alternatively, if you're wanting to do something more aggressive, you could consider a balanced fund, such as Vanguard's LifeStrategy Income Fund (VASIX), which is 20% Stocks / 80% Bonds.

Alternatively, anyone know of any genuine private lenders that are open to this?

Here in Michigan, it’s not as easy, so I’m exploring alternatives.

There are hardship withdrawal provisions and others that can be exercised if you meet the requirements. 3) If you have access to a workplace plan, like a 401k, with a Roth component, you can consider that as well. 4) If you setup your Roth with a Self-Directed IRA custodian, they can allow you to invest in assets like real estate, private lending, private equity and other alternative assets. 

Are you suggesting this as an alternative to taking a period of time to save up the capital?

I think it is easier to find a deal if you are house hacking since your deal doesn't need to be a home run; it just needs to be better then the alternative (paying rent).

is there an alternate use to put in there following the restaurant. 

As an alternative you could look for a walk-out, lock-off basement and add a small kitchen/kitchenette down there to have your own space away from your housemates.