I won't disagree that putting a credit card form up is a barrier, principally because constructing barriers is the point of the exercise. Net-net, it strikes me as better to inconvenience a fraction of users predictably with mitigation in place versus inconveniencing all users unpredictably in a difficult-to-recover-from fashion when e.g. your hosting company sends you a termination letter.
By the way, since you mention you haven't worked in hosting before: you should know that you're at risk of getting your account terminated, even if you answer all tickets in a timely fashion. Every ticket opened against you represents multiple fairly highly-paid humans having to interrupt their work days. They accept this as a cost of doing business the first few times. You will eventually be told "You don't pay us nearly enough to generate this volume of tickets. Take your business elsewhere."
Anyhow, your business, ultimately your call. If you're looking to do primarily automated solutions:
1) Risk score customers. You can do this in intelligent, data-driven fashions, but you'll get results quicker by just coding heuristics. Some heuristics which you'll find valuable are "Where is the ngrok client getting called from? Does it come from a number of high-risk countries?" (I know, I know, most people hate the implications here but it is a case of being mugged by reality), "What OS are they using for the client application?", "Has the machine invoking the current ngrok subdomain been banned before?", "Does the subdomain receive traffic from 'far away' from the IP we're sending it to?", "Does the subdomain receive traffic from more than N IPs?", "Is there a large lag between creation of the subdomain and first use?", "Does an IP create multiple subdomains either in parallel or in series?", etc. You can easily make people's access increasingly open as their risk score approaches Presumed Safe and make it more restricted as their risk score approaches Quite Possibly Not Safe. (This is a nice compromise which lets legitimate users without a credit card in without-loss-of-generality China continue to get non-zero value out of ngrok.)
2) You may wish to have your client application fingerprint systems which it is installed on. (There exists substantial literature on this.) Add abusers' fingerprints to a hellban list: their IPs can see their sites, and maybe the first 3 IPs accessing their subdomain see it and get added to a bucket which shares their hellban, but everyone else mysteriously 500s out. This will make it hard for abusers to realize "Doh, I have been found out and need to switch proxies or rooted boxes."
P.S. Customer to vendor here: irrespective of your decision with regards to people who don't pay money for your services, please charge more. It will give you more resources to fix this problem so that you don't get shut down again and ruin my Twilio programming productivity.