Phone IRC apps are the most annoying things in the world. Constant join and part messages as they disconnect and reconnect. That's one advantage of things like Slack; they handle persistence at the server level, rather than relying on the client. That being said, I'm a huge IRC fan and use it at work all day every day on two internally managed servers.
IRCCloud
I agree there. I dont worry about anything with irccloud. You might be able to achieve the same with a bouncer but then you still gotta invest in hosting one too.
If you don't want to pay for IRCCloud I would totally vouch for Matrix. I've hosted Quassel, ZNC and The Longue and different times but moving to Matrix and their IRC bridge has made my life much easier.