The last two tax lien houses that I got and sold had major plumbing issues.

For now all you are going to see is more of the same because the vast majority of inventory is being held by people with 4-sub 4 rates and they can't/won't want to afford elevated prices and 6+ rates.

For example, they lost a fairly major battle when they tried to argue that only licensed professional can manage short term rental properties. 

The above two are your major liability determinants.  

Along any major road heading out of the city.

:Class A Properties:Cashflow vs Appreciation: Typically, 3-5 years for positive cashflow, but you get highest relative rent & value appreciation.Vacancy Est: Historically 10%, 5% the more recent norm.Tenant Pool: Majority will have FICO scores of 680+ (roughly 5% probability of default), zero evictions in last 7 years.Class B Properties:Cashflow vs Appreciation: Typically, decent amount of relative rent & value appreciation.Vacancy Est: Historically 10%, 5% should be applied only if proper research done to support.Tenant Pool: Majority will have FICO scores of 620-680 (around 10% probability of default), some blemishes, but should have no evictions in last 5 yearsClass C Properties:Cashflow vs Appreciation: Typically, high cashflow and at the lower end of relative rent & value appreciation.

You can certainly buy the property in the name of the LLC but you'll have to use a DSCR product which will have an interest rate that's 1% higher than conventional. 

Is there a combination of lending products and tactics you see that can make it possible to refinance after possibly 2 years and get out a large enough portion of funds to use towards the downpayment on another property?

Another way is to switch your product from 30 year fixed to a 5/1 ARM so now you're taking program or financial risk to arrive at a lower rate such that you can pass this FHA SS rule (5/1 ARM FHA has a lower rate by up to .50% than the 30 year product typically).

Also you can see their overall productivity.