From what I understand, you want to "get it out of the way", because you want to focus on the song writing aspect, but not get too in depth with piano technique intricacies. What most people are trying to tell you is that even learning the basic skills, techniques, patterns takes quite a lot of practice and time, because piano is not by any means a simple instrument. Even if you develop a basic level of piano skill that allows you to comfortably write songs, you will most likely be stuck at that level until you continue to learn piano properly. Many of the current industry pop artists that use piano, all started from learning classical music and from bottom up.
That being said, I believe there are ways that can allow you to familiarize with techniques and patterns quickly without diving too much into theoretical knowledge (although some may disagree with my points).
- The first thing to write pop music is to listen to it. Listen to a lot of pop music with the piano and actively listen to it (as opposed to passively). Active listening means you're listening to the music intentionally and while doing so, try to analyze the piano part specifically for the chord progressions, scales, arpeggios, key rhythms. Also try to compare songs, because most general pop music uses similar chord progressions.
- Play and practice the piano by imitation and replication (ie. play the piano while you're playing the music track from your computer/youtube, etc...). Obviously, if you don't have even rudimentary skills, this can be hard, but you know scales and chords so it should be okay. Start with music pieces that use simpler and slower piano tunes and work your way up to something more intricate (like Vanessa Carlton's
A Thousand Miles, which is a fantastic piano pop song btw). If you have trouble with even simpler songs, then start by focusing on just the melody lines. If you know how to read music, it would also help if you can find sheet music versions of those songs and give those a try. Doing this replication is helpful because it helps you associate the sounds and patterns you hear with actual finger/hand movements.
My answer is based on my experience currently learning the bass guitar. I couldn't stand practicing just scales and playing random notes and tunes from the back of my head, while a lot of the beginner tutorials were just to simple. So instead I just started trying to play the bass parts of actual songs, which is a lot more fun and it seems to be helping me learn faster. However, I do have years of experience with the piano, so I would think my faster learning at the end of the stay still attributes back to the sweat and tears from piano practice.
At the end of the day, even the points I mentioned will take some time and I agree with all the comments in the question, that there are no shortcuts in life. You may end up learning the basics, but it won't mean you understand it (ie. You may know a chord progression but don't know why a certain chord progression sounds good). Writing industry level music doesn't take days, weeks, months and if you want to learn piano so that you can progressively get better as you write music, the only way is through learning piano properly.