Is there a way to assign an ATM Strategy in NT to an order entered via the DOM in Jigsaw?

E.g. I want an order to start with something like an 8-tick stop, moving to a 4-tick trailing stop after the market moves 5 ticks into profit.

Sure it can be done.
In Daytradr the first icon from the left is Connection, the following icon looks like umbrella with a gold coins. It is a strategy manager.

This is what you need. Here is the link to help you out: https://daytradr.jigsawtrading.com/strategy-manager.html.
It is very easy to configure.

I hope it helps

Feel free to ask any question if you going to face any issues with it.