How do I capture custom payment later than the authorized amount?

I need to get payment authorization but I cannot pre-select the amount to be charged because it depends on when and if someone drops out of our program...

I run a teaching fellowship and teachers receive an all-expense-paid experience with us UNLESS they drop out. If they drop out and are booked on one of our group flights the drop out fee is only $250 but if they used their stipend for customized travel, the drop-out fee is whatever they used of the stipend, up to $1650. On the payment authorization threads it seems as if a specific product or amount must be authorized. Is there a way around this?

Correct. The payment gateway allows to capture the amount which is authorized while submitting the form. However, using PayPal method you may consider getting the authorization for the highest amount and you may charge lesser by customizing in the PayPal dashboard.

https://www.jotform.com/help/292-How-to-Enable-Payment-Authorization

Please give it a try and let us know if you need any further assistance. We will be happy to assist.