The fact that the data changes each time a client accesses it is not a reason not to use GET. You are not POSTing any data to the web server, you are merely GETting the current state of the resource. That state may be constantly changing, for example
GET /currenttime.html will constantly change each time you request it. There isn't anything in the HTTP spec that says that a client should expect that a resource does not change between GETs. The server can update the resource what ever way it sees fit, either internally or due to other clients updating the resource. A client should never assume that a resource has not changed since it last got its state.
It is though a reason to use an ETag in the response header to let the client (and any caching in between) know what the server has changed the resource since the client last accessed it. A client can compare the ETags to know that the resource has changed.