Temporary redirect traffic to specified origin via header or cookie

I’m evaluating Cloudflare Load Balancer to see if it can help me address read-after-write-consistency use case.

I have an app server with a primary db, and many geographically-distributed app servers connected to local replica dbs for fast response times.

I plan to put all app servers behind a CF Load Balancer and use Custom Rules to ensure that it steers all POST/PATCH requests (I.e. write requests) to the primary app server and that all GET/HEAD requests are steered by proximity/geo to an app sever closest to the user (this is possible, right?).

However, after a successful db write to the primary db, I would like to instruct the client to continue sending all subsequent GET/HEAD requests to the primary origin as well for a brief period of time (e.g. 5 seconds) instead of to the closest origin, until we are sure the newly written data has propagated to all the local replicas and user doesn’t see 404s.

My question, is it possible to set such a cookie or request header on the client, that if present during a request to the CF Load balancer, it will instruct the Load Balancer to hit the origin specified in the request header or cookie?

Is that something that can be solved by Custom Rules again or by Session Affinity?

Many thanks!