Airdriod for me and note to D.O., airdroid does not require a rooted phone. Been using it for years and I prefer it because it does a whole lot more than just texting. Never once used their web based service to connect through, always used a regular wireless Lan.
However, there's an easier way, much easier cause you already know how to do it. Now that Googles voice to text has improved so much, with the proviso that you have an active internet connection, it's almost entirely possible for you to do most of your messaging by dictating to your phone in natural speech.
Open your messaging app, start as you would to begin typing, but instead of typing, have a hunt around your tiny keyboard for a microphone icon. If you don't see one straight away, it may be hidden under a gear or a T key with some extra tiny things on the same key. You could also just install and switch to the Google keyboard and do away with the clumsy keyboard jammed in there by the phone manufacturer cause the google keyboard has a permanent microphone icon at the top.
Anyway, once you find it, tap it, wait a second or 2 and start talking, but don't robotise your voice, speak normally, but clearly and annunciate your words. Provided there's not too much background noise, your words will be converted to text with amazing accuracy. However, with such a great tool, there's always a caveat, it doesn't know how to abbreviate or accent what has been translated, but that's dependent on android version, learnt patterns and other variables.
When finished speaking, press the stop button or an x in the listening window and edit or send your text.
Here's a vid on how to do it