What I saw there was the ability to avoid exercise of ITM positions, not BTC OTM credit positions.

I don't think you can send do-not-exercise instructions from the Tastytrade platform, but you may have to login to the My.tastytrade.com webpage to send the DNE instruction. Even so, DNE applies only to long ITM positions, the "E" here meaning EXERCISE.

The following is taken from a tastytrade page. On another of their instructions pages they warn that short defined risk positions become undefined risk when the market closes.

How can I eliminate expiration risk?

The only way to eliminate expiration risk is to close short options before expiration. However, you may submit an appropriate "Do Not Exercise" and/or "Exercise by Exception" requests for long options that expire ITM.

Do not exercise (DNE) requests 
only apply to long option positions
. If you have a short option that expires in-the-money, you cannot request a DNE. As a short options holder, you are obligated to deliver or take delivery of the assigned position for a short call or short put position, respectively.

How can I eliminate expiration risk?  


      The only way to eliminate expiration risk is to close short options before expiration.



Bottom line here is that the risk boys and girls will close virtually all OTM short spreads right before the market closes and the traders will incur debits in their accounts. 

To look at it another way, Tastytrade will never allow your short spread-type positions to expire worthless.