As the 90 day report is also asking for your current address, you can do it everywhere in Thailand AS LONG AS your address is registered at the same Immigration Office.
There is NO rule that forbids you to travel or change address during one year, you are not obligated to make the 90 day report at the same office where you got your Extension of Stay
IF you use the on line method, you can fill in your home address even when temporarily residing elsewhere in Thailand
Show us the proof that you can NOT get a 1 year Extension of Stay after you got a 60 day Extension of Stay based on visiting Thai family.
I understand your story as the Extension of Stay "60 day friends and family Extension" does not exist and therefore can not be issued.
It is a common practice when the foreigner did not have time enough to deposit his money into his account, to gain extra time, first the 60 days based on visiting Thai family than the 1 year.
So first you tell "Ï've tried" than it becomes you have different info from friends to end with you have this info straight from the Immigration.
As you switch every time to make a point, I would say share this direct information from Immigration, the Police Order as that is the only correct way.
Not I have tried, i hear from friends or I talked with the cleaner of the office and now I tell you the law changed.
At entry into Thailand during the visa validity you get a 365 days of Admitted to stay OR until the last day of your health insurance, which ever comes first.
So be aware that you have at least a 1 year valid insurance if you want to re-enter Thailand during the visa validity.
At arriving at an address you need to report that stay at that address at the local Immigration Office, your hotel or land lord may do this but discuss this with them.
IF you stay 90 days consecutive inside Thailand you need to report this at your local Immigration Office.