I have tried the likes of Binance and Bitterex, but they aren't accepting any new users at the moment.
What do you mean by this?
AFAIK, Binance always accepts the new registration (except for the restricted area).
Where do you live? If you are in the US, you can go to the Binance US and get the registration in this
site.
As in my country, Binance site is forbidden so that I can only use the Binance application or change my DNS point to be able to access Binance.