You’re coming up against DNS specifications where a naked domain cannot point to a FQDN and must instead point to an IP address.
This is a restriction that your customer will come up against in the configuration of their domain and there’s not a lot you can do. I would suggest that you require your customers to use a subdomain (even if it’s www).
If you require your customers to use a subdomain, you can tell them to set up a record like this:
appsubdomain in CNAME user2customdomain.saas.com
Then when you later change your IP address, you can update your A record (or preferably a subdomain wildcard) to the new IP without requiring your customer to change any DNS.
If you need your customers to be able to have a CNAME at the root of their domain, the best you can do is direct your customers to switch DNS. (This might be a hard sell.)
Zenfolio.com is another SAAS service that allows you to set up their service at your own custom domain. Here’s their instructions: