A method may be provided in a wireless terminal to modify access to a Radio Access Network. The method may include providing a barring rate at the wireless terminal and providing a barring rate modifier at the wireless terminal. A modified barring rate may be provided at the wireless terminal responsive to the barring rate and the barring rate modifier with the modified barring rate and the barring rate being different. A random number may be provided at the wireless terminal responsive to attempting to access the Radio Access Network, and access of the wireless terminal to the Radio Access Network may be blocked responsive to the random number failing to satisfy a threshold of the modified barring rate. Related wireless terminals, network nodes, and network operations are also discussed.