The differences are these:1 - Equity is dead until you access it, when it becomes cash...the same cash that you originally had before you transferred it into equity. 

Box; rent can only be paid by bank deposit.For your convenience, the nearest location to your home is 123 Main Street, (City), or you can execute a bank-to-bank transfer using the routing number provided.If you have any questions, concerns or maintenance issues, you may call or text my cell phone at (your business number), or you may email me at the address listed at the top of this notice.Please don’t hesitate to contact me with any questions about this transition or any other pertinent issue.Sincerely,(you)

It separates the liability.I'm not sure what you are getting at with "If it goes well, the home title can be transferred to an LLC." 

There's one house titled to Rad Diversified REIT Inc and it was nominally transferred from an affiliate company for $1.

I'm considering assuming this mortgage, either "subject to" or by transferring the property into a trust, where I would then buy a majority share and cover the remaining balance in cash.The complication arises from the fact that this existing mortgage is a VA loan.

It's not, we'd have to transfer the title? 

Whilst legally this should trigger the sale purchase clause and put you in breach of contract, both of them admitted that the transfer is a common occurrence and not a big deal.

., anonymity of ownership, avoid doc stamps with encumbered real estate, avoid personal judgment liens from attaching to the real estate, buying at auction, keeping transfers private. 

In parallel start talking to other potential candidate GC’s to see what their costs and schedules would be like (make sure you ask them how hard it is to transfer permits).  

Look for military and civilian workers selling their homes, for transfers out of town, or trade ups for bigger homes.