Send him a polite email that you have refunded two months which goes beyond the terms of service of 30 day refunds and thank him for trying out your app.
If you can see what type of card he used you could call their customer service and try to find out how long they have to make a chargeback and then refund back to that date if it's 120 days, refunding three payments might cover it or 90 days two payments might cover it depending on how long this discussion has been going on.
On the other hand if $1000 won't make or break your cash flow just refund the whole amount so he'll go on his merry way and maybe you can avoid a negative evangelist for your app. Plus chargebacks are going to cost you fees and time/hassle.
Sometimes you just run in to problem clients as a consultant and SaaS owner.
Good luck closing things out with him.
The ones that you know deserve a refund are easy to give it to because you feel it in your bones that it is the right decision, don't question yourself on those. The ones like this person are not being reasonable, but throwing them a small bone is a minor factor. From my own perspective when a client is obviously being a jerk and threatening legal action, I generally say something to the affect, "I am sorry that there is nothing we can do for you at this point given your position". Sometimes I will point out to them that based on the T&C's they agreed to that their legal fees will be significant considering that when I prove they are in the wrong based on the agreed to T&C's, they will also owe all my attorney fees and costs.
Bully's consistently back down to one thing, an informed person that is willing to meet them head on. Usually the calmer you are, and the more reasonable but extremely firm in your position the better.
I was in my personal attorney's office one day when he got a call from a large enterprise that he had already sued and one a settlement against for his home siding that apparently was defective. They were trying to get him to also sign away more rights and agree not to represent anyone else or share any information about his case, and they wanted a joint stipulation to seal the case. I loved his response to their attorney on the phone, he said, well, I could do that, or I could form a class action suit against you for even suggesting that other people don't have the same right I did to a refund and damages. One bully vs someone unafraid, the company backed down and cut him a check and he made the case public but didn't go after the company anymore. Just always sat with me, he never yelled, never got offended, just made is position extremely clear and unwavering.
Try to hold out and not give a full refund, I say this for two reasons. First is the principle, Second is for the potential legal situation it puts you in. Yes, you have the right to make almost whatever decision you want, however, if you refund his entire amount then the next jerk that comes along may use it as a point that you violated your own T&C's, so he deserves his full refund too. I am not an attorney so you could ask one for specific advice, but I have been told that exact thing more than once by my own attorney. He constantly tells me to make sure I hold people to the T&C's and that I shouldn't "violate" them either without extenuating circumstances which can be documented to prove a unique circumstance that warranted me doing so.
Good luck no matter what.
he is claiming that his bootstrapped business failed some deadlines and deliverables because of us, lol really. That is just hilarious.
He is claiming a lot of things honestly and it is just plain lie. The question here really is: Should I continue doing this back and forth fight with him or just pay him the entire refund ? I am offering him last month's refund as a token but even that is against the terms and conditions.
That is very generous of you. If he was not happy, he should have cancelled in 30 days. I wouldn't go back and forth with him nor would I give him a penny more if I were in your shoes. You are in to make a profit as well. Imagine if all your customers did this? Stand firm and don't give him a dime.
Good guy you are. Stand firm and call his bluff. 5 months is a long time to not realize something isn't working for a business.