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Thanks for posting here.
I understand that you are transition from OLSB and would like to use the custom domain in SharePoint Online public-facing website without Exchange Online mail service. I have tried to access your website with the URL: www.hawkinsaccounting.com and get a no longer available page as mentioned.
In general, as soon as you remove your domain name from Office Live Small Business, your domain name will no longer point to the website that you created in Office Live Small Business. So, it will be displayed as no longer available page. Based on the current situation, I would like to confirm if your domain has been added to Office 365 successfully.
If it is true, to use this custom domain in SharePoint Online public-facing website, please refer to the following steps:
1. On the Office 365 admin page, click Domain, and then click the button Change address. Then, a CNAME and A record for this domain will be created by system automatically.
2. Select the added custom domain, and click Manage DNS, then gather the CNAME and A record information created by the step1.
3. Add the corresponding DNS records at your domain registrar.
Typically, it may take about15 minutes, but can take up to 72 hours for the record that you created to propagate through the DNS system.
Just check in to see if the information provided is useful for you.
If you need addition assistance, please feel free to post in the forum. We will be more than happy to be of help.