They then transfer the loan to Fannie or Freddie where it is bundled up with a bunch of other loans with similar credit/debt to income/loan to value characteristics and sold to institutional investors as a bond (mortgage backed securities). 

Class B properties are typically owned by Institutional investors and private investment groups, or very high net worth individuals.

As a subject matter expert for a major lending institution and over 20 years in the industry properly executed "assignments" are not a problem. 

They target more for institutional money, but the concept is the same.

However I feel like another institution could probably use that rental income?

Thanks For an institutional lender, we're going to look at the total value of the properties as opposed to the dollar amount of what the value is vs what is owed.

It's greatest value is to the charitable institutions that market them to secure assets ahead of a benefactors demise (cynical snarl - mine).  

I shopped for which institution I would use years ago and found my credit union that doesn't charge me any fees, logs in a comment in which building and unit paid, mail me the receipts, and it works quite well.

Does anyone know of a financial institution that will do construction financing in this situation?

The Self-Directed IRA and Solo 401k DifferencesIn order to open a solo 401k, self-employment, whether on a part-time or full-time basis, is required;To open a self-directed IRA, self-employment income is not required;In order to gain IRA checkbook control over the self-directed IRA funds, a limited liability company (IRA LLC) must be utilized;The solo 401k allows for checkbook control from the onset;The solo 401k allows for personal loan known as a solo 401k loan;It is prohibited to borrow from your IRA;The Solo 401k may be invested in life insurance;The self-directed IRA may not be invested in life insurance;The solo 401k allow for high contribution amounts (for 2016, the solo 401k contribution limit is $53,000, whereas the self-directed IRA contribution limit is $5,500);The solo 401k business owner can serve as trustee of the solo 401k;The self-directed IRA participant/owner may not serve as trustee or custodian of her IRA; instead, a trust company or bank institution is required;When distributions commence from the solo 401k a mandatory 20% of federal taxes must be withheld from each distribution and submitted electronically to the IRS by the 15th of the month following the date of each distribution;Rollovers and/or transfers from IRAs or qualified plans (e.g., former employer 401k) to a solo 401k are not reported on Form 5498, but rather on Form 5500-EZ, but only if the air market value of the solo 401k exceeds $250K as of the end of the plan year (generally 12/31);When funds are rolled over or transferred from an IRA or 401k to a self-directed IRA, the amount deposited into the self-directed IRA is reported on Form 5498 by the receiving self-directed IRA custodian by May of the year following the rollover/transfer.Rollovers (provided the 60 day rollover window is satisfied) from an IRA to a Solo 401k or self-directed IRA are reported on lines 15a and 15b of Form 1040;Pre-tax IRA contributions on reported on line 32 of Form 1040;Pre-tax solo 401k contributions are reported on line 28 of Form 1040;Roth solo 401k funds are subject to RMDs;A Roth 401k may be transferred to a Roth IRA (Note that from a planning perspective, it may be advantageous to transfer Roth Solo 401k funds to a Roth IRA before turning age 70 ½ in order to escape the Roth RMD requirement applicable to Roth 401k contributions including Roth Solo 401k contributions and earnings.)