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A custom subdomain in front of your tagging server is the single biggest configuration win, and DNS is the only part that takes any real time.
If your tagging server is still answering on the default *.run.app hostname, you are leaving conversions on the table. Ad blockers know that hostname. They do not know data.yoursite.com, which is the entire point of doing this.
Anything that does not look like a tracker survives longer. Good choices: data, events, metrics, api. Bad choices: anything containing the words track, analytics, gtm, or ga.
In your DNS provider, add a CNAME from the chosen subdomain to the tagging URL shown in your SprTags dashboard. Cloudflare users should set the proxy status to grey-cloud (DNS only); orange-cloud will break the SSL handshake on the upstream container.
From a terminal, check that the hostname resolves and returns a 404 from gtm.js when no preview header is sent:
dig data.yoursite.com +short
curl -I https://data.yoursite.com/gtm.js
A clean response with a Google-issued certificate means SprTags has provisioned SSL and you are good to point traffic at it.
In your client GTM container, open Container Settings and override the GTM JavaScript source. Use https://data.yoursite.com as the base URL. Publish a new container version. Live traffic will pick up the new loader within minutes.
If something looks off after publishing, the most common cause is a CORS error from a stale CSP header that still references the old hostname. Once that is updated the recovery is immediate.
When this is in place, the next thing to set up is preview mode against the new domain, then start migrating tags one at a time.