I wonder if I have too much going on in the left hand that it detracts from the melody ?
I like the left hand accompaniment, and it doesn't seem to me that it gets in the way of the melody at all. What I can't tell from the recording, though, is what kind of balance you're getting. It sounds as if the microphone is placed very close to the right side, so that the left-hand chords sound quite subdued (maybe even a tad too subdued) in comparison. Since your own ears are more or less equidistant from the two sides, your impression of the relative volumes may be more accurate.
On the other hand, concertinas, because of their construction, are unusually tricky this way. I've played in more than one session where I could barely hear myself, only to be told later that mine was the loudest instrument in the room. When you're playing in the harmonic style a listener on your right (like us, in this instance) may hear the melody loud and clear, while one on your left is hearing only loud chords. If you're playing without amplification for a live audience, every one of your listeners is getting a slightly different mix.
When you record yourself, your microphone placement (assuming you're using just one) can be used to optimize the balance. But if you think of recording as an approximation of live performance rather than an end in itself, that strategically placed mic may give a very misleading impression of what most listeners would hear.
I wouldn't change your approach to accompaniment; it's quite lovely. But if it seems to *you* that the chords are obtrusive, you can try playing them with a lighter, more staccato touch. And if you want your recording to give a more faithful impression of what a live listener would hear (assuming s/he isn't next to you on a bench), try facing the mic from a slightly greater distance.
I use a Tascam multi track recorder for recording. It has twin built in condenser mics and I sit with the recorder in the middle of the concertina and record the left and right mics onto separate tracks. If I'm multitracking, other instruments are added on other channels and when I mix the resulting recordings I pan the two concertina channels slightly apart from each other so you hear the sound from the two ends coming from different places in the stereo space. The built in mics are omni directional and will each pick up both ends of the concertina but the overall effect still works well as each mic will "hear" more of the nearer side. The main thing is not to pan the two tracks too far apart from each other to get the right effect.
In the case of The Wren, I used the smaller of my two Tascam recorders which has two mono and two stereo channels. I recorded the concertina on the two mono channels and then "bounced" them on to one of the stereo channels panning them about 20% to left and right. I then reused one of the mono channels to record the ukulele and when I finally mixed the two instruments, I panned the ukulele about 30% left and the concertina 30% right of centre but the concertina itself still had that bit of width.
Concertinas in sessions are difficult because it's hard to hear yourself. I've noticed a lot of concertina players in sessions hold the instrument with their arms vertical so it's near the face so they can hear themselves. I mostly take harmonicas to sessions as I can hear what I am doing and also I find I am better able to pick up tunes I don't know and join in - as long as they play enough times through. The issue you mention of what you hear from others in a session is true of all squeeze boxes. You tend to hear the end nearer you.