How to set value on other dialog elements

I want to update multiple text areas from one script in my service dialog. I know I can read other text areas using $evm.root['dialog_field_name'], but setting them from a script is not so straightforward.

Here’s what I’ve tried:
$evm.root['dialog_field_name'] = 'new value goes here'
$evm.root['dialog-field-name'].value = 'new value goes here'

Neither worked. The second gave “undefined method error”.

Any ideas? Is this not possible? Thank you.

PS: I know I can chain these other text fields to run their own scripts, but I’m struggling to pass a value from one to the next. See related question here.