I just checked that link and currently the server does not appear to be started - I searched in the station list and couldn't find you on there.
Tunein does accept icecast streams as I flipped my server over from shoutcast to icecast and I'm still on there with VFR Europe (even during a point when my playout was completely screwed and I had to revert to Centovacast); I did resubmit the streams with the mountpoint and I'm still not sure if they recognise my aac transcode for mobile users.
I think you may have to register with them as a "broadcaster" to get certain updates; not tried it so not sure if there are any costs involved.
there has always been one menu on centovacast where its very easy (particularly if using a laptop with touchpad) to accidentally shut off your server once more instead of restart it. I often suggest buying a £5 mouse from ASDA and keeping it handy for working on "dangerous" screens like this.
Also a raspberry pi is dirt-cheap; doesn't use much leccy even if left switched on 24/7 and will run vlc media player from the command line; you can use one as a silence detector alarm which may come in handy if you are usually a 24/7 station