Every free centralized messaging service at some point needs to find a business model that finances the platform. Right now the (IMO) best choice are decentralized messaging protocols such as XMPP (https://xmpp.org/) or Matrix (https://matrix.org/). Similar to email you can (i) run your own server or decide which server to use (ii) communicate with people on other servers, and (iii) choose from multiple independent client and server implementations.

For XMPP I recommend Conversations (https://conversations.im/) as client on Android and ChatSecure as iOS client (https://chatsecure.org/). An simple easy to use server implementation is Prosody (https://prosody.im/), but ejabberd (https://www.ejabberd.im/) is a good choice too. There are also multiple public servers if you don't want to run your own server instance, for example the XMPP server run by DuckDuckGo (https://duck.co/help/community-platform/xmpp).

For Matrix Riot is the best client implementation which runs on multiple platforms (https://riot.im/). The (afaik) only usable server implementation is the reference implementation (https://matrix.org/), but at some future point the currently pre-alpha Rust-based Ruma implementation (https://www.ruma.io/) could be a good choice too.

A nice thing about XMPP is that server-based transports can provide gateway-functionality to other networks. For example with Spectrum (http://spectrum.im/) it's possible to use your XMPP client of choice to chat with your friends that use Facebook Messenger.

The problem is that many of my friends aren't going to switch. Using a gateway/proxy is good until the banhammer comes down.

It's looking like my best option is to buy an iPhone for an iMessage/Signal one-two punch.

Twitter doesn't put ads in direct messages. I haven't used Snapchat or Allo myself, but the other ones I said I use don't have ads in messages.