However, I just received the closing docs, and the rate on the 6.9% loan has been increased to 7.8%.

If you decide not to renew their lease or increase their rent they need a 60 day notice, and you have to notify S8 as well.Outside of those 2 exceptions your tenant should follow the lease like everyone else.

The key lesson is that if you rent to Section 8 tenants, their negative behaviors may result in non-Section 8 tenants to leave.Rent increases are more likely tied to the minimum wage.

Is there a way to increase the cash flow from those?

Each market is different but as a national average, the increasing rates have increased the inventory.

The mortgage has gotten out of hand due to property tax increases, miscalculated escrow, and an increase in my interest rate from an initial buy down, increasing from $2600/mo to $3200/mo.

Pretty much the core of the STR business.Higher your rank gets, you can increase your price and be more picky in selecting customers which usually lead to a better review / less party or complaints / less expense and higher profit with a happy life.I know some people will argue, but the ranking system is the truth and should be the only guide to your STR journey. 

I'm also not super optimistic on rents increasing over the next year or two though, especially if we go into a recession.

Quote from @Rich Davis: I know there have been posts regarding the ever increasing cost of insurance.  

Here is my case for over valued in general:- over a decade in f unprecedented price increases- rates have doubled significantly raising the cost of a high LTV purchases, but in most markets there have been no corresponding price decrease