It was really bad during the Hurricane Harvey's time and found similar problem in 42, 44 which is better. Your observation is correct, if connected to wi-fi or hot spot LTE, there's no problem. After updating to 44, one day I have to reboot all computers to get back to LTE after stuck at 3G.
SA told me before that's Tesla server and firmware related, i.e. if using Tesla onboard LTE, somehow the traffic has to go through Tesla's server instead of direct internet connection to Tunein/Slacker. Either they are caching something on Tesla side or proxying through Tesla, that makes it problematic. Another problem never resolved is - it cannot automatically reconnect after switching from wifi to Tesla LTE, eg. listening on Tunein in the garage, drive to work and after 100 ft, it loses wifi connection, whatever I am listening on will spin forever unless I switch to other thing and back.