February 2020 - last edited February 2020
I can confirm that this works. For anyone using Geforce Now still receiving the 'Too many computers..." error, simply login to your EA account, navigate to "Security" tab and click on "Login Verification". Choose email, phone number etc.. EA will send you a verification code to your communication option of choice. Enter this code in the box. Once complete and verified, login through Geforce Now again with your account, it will ask you to verify again via your choice (Email, phone etc..) Enter the next code, and you should have no problems.
The issue is GeForce Now logs each session as a virtual computer in a different location each login, which Origin/EA flags as suspicious. No need to wait 24 hours with this method though
As a note: You will have to re-verify each login! this will not permanently fix the problem or allow you to fluidly pass through the Origin login process when playing Apex Legends. However, it is a temporary workaround. Also, it is possible you will have to occasionally login to your EA account, navigate to "security" and under trusted devices, choose remove trusted devices. EA/Origin, please fix this issue regarding GeForce Now compatibility.