Got it. Yeah it's strange Assigned To isn't an option here in approval processes:

Is there a large amount of people that would be receiving these approvals? If it's manageable, you could create pre-set task approvals that the person completing the form and passing off to the person for data check just selects the correct approval flow? So 'Sarah Approval,' 'Ted Approval,' etc. Of course not a realistic option if you have too many people.
Are your templates people specific? If X template will always need Sarah's approval, you could work it into the template task's approval flow. If Y template always needs Ted's, you include that in the other template, etc.