> Using the browser no longer work for reading these messages, since they are pushing the Messenger app.

Ditto. Works for me, too. I use FB.com to see messages on mobile Safari.

The only reason I don't use FB.com for everything is cause FB app allows me to upload video (but since I can't seem to get video posted to FB, via my iPhone 5C, to come out nicely, I'm going to delete the app too).

On Chrome on Android, at least, if you don't use "Request desktop site", you can't get messages on messenger.com or facebook.com (the messages icon doesn't even show up on the latter, and the former just directs you to an app download.)

You can use "request desktop site" on messenger.com (and probably also facebook.com), or use mbasic.facebook.com to get messages without the messenger app.

Here's what I get when I try to view my messages in the browser on my phone: http://m.imgur.com/oSuv6NH

If you force the desktop version of the page it works, but is awkward. Instead I use a web wrapper that has some other nice features, like showing me my messages with formatting that scales well to my phone's screen size

My bad, I only considered desktop access. I'm interested to know the name of he wrapper though.