How to justify not using a certain program or API or framework because it is not free
Most of the reasons you gave in your post seems justifiable enough. I'll just list them to make it clear. 


You have sufficiently abled tools to solve your objective without the proprietary tool. 
You don't have a funding to cover the expense of certain proprietary tools. 
You are able to use limited licensing to cover up most of the commercial options.   


Apart from the good excuses, you could at least request the tool provider to see of they would sponsor you with a temporary research/student licence (or a similar sort) by stating your objectives.