They bought out another registrar I was a customer of. Now I am paying 40% more for renewals. If I want to migrate I need to expose my whois info. They're always looking to upsell me into some horrible hosting garbage.
Update your whois to bogus information, transfer the domain, restore whois information. Cloudflare is the cheapest domain registrar long-term, you might get cheaper ones for the first year or first 3 years.
Using bogus whois info is a great way to lose your domain. If you are afraid of exposing your phone number and address, rent a P.O. box and get a throwaway number to use in the interim.
You will not lose your domain for having bogus information for 7 days. Having bogus information takes months of not an entire year to ever go through and the worst you will possibly get is a very stern warning to update your information or your domain will be taken away.
I still have a .com domain that I've registered from when I was a child and I've just never bothered to update the information on it, the regulations on these are as lax as godaddys security.
If you're a site with millions of views a day this might be different.
It's called the 60 day registrant change lock. Most changes to administrative or technical contact information will trigger it.
Although it's a real ICANN rule, the registrar is allowed to override it if they want. Of course very few registrars offer that kind of customer service, so that escape hatch might as well not exist...