Student loan payments have crippled my ability to save, which also limits my options. 

I don't know if you have a specific reason for using an IRA vs. self directed solo 401k - if you can go the 401k route (self employed) then you have some serious benefits such as much higher contribution limits, less reporting requirements, more investment options etc.

What is the annual loan limit?

I'm about to close on a fourplex with a hefty pest report, but only a limited amount that's structural. 

I'm closing on a property with existing tenants (in Oakland, rent controlled). 

I think it would be wise for me to partner up with this small group because of my limited experience, knowledge, and funds.

You can refinance immediately with no seasoning using the current appraised value however you are limited to 75% (not 70% as alluded here) and the total new loan cant exceed your initial acquisition + closing costs.

@Russell Brazil and @Jon Holdman thanks a lot, I didn't know that there is a clear wear and tear limit for carpet at 5 years, very useful info!!  

Unfortunately though, the supply appears to be rather limited in the Jacksonville area and most of these properties are located in what appear to be questionable neighborhoods - class D. 

You may be able to get into something there-there are a lot of owner occupant loans with very favorable terms and they are not just limited to FHA.