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I'd feel inclined to put this down to being part of the never ending learning curve. If it makes you feel any better I did the same - but on very long runway ...but wondered why we casually drifted past the exit I usually would use still 2 feet off the ground ! I aslo did the opposite in training once - why aren't I climbing properly? - oh full flap still on a touch & go - oops ! ( again a long runway so nota problem in that situation ) - My FI knowingly allowed me to do it so I'd remember - which I did :)

I went to a system of one stage at a time on Pa-28s after that - one stage pulled in or removed , hand off the lever , check , then back down to the next stage , again hand off , check and pull again if needed.

I guess you learn , you make a mistake , you learn , you move on , you make a different mistake until they become so rare you have then properly 'learnt to fly ' .
When doing a go-around with a PA28 (of which I do a handful each year) I build some speed and then go from three stages to two. I then build speed to 80 kts, start the climb and then continue like a normal shortfield take-off where the rest of the flaps are retracted at 500 feet AGL. If obstacles are an issue, I'd use Vx instead of 80 kts in the climb.
Different PA28s are different, but you really need to be removing that third stage of flap immediately, as you'll struggle to accelerate at all with it deployed - it mostly provides drag rather than additional lift.
Its Full Power (and carb heat cold), check attitude (especially if you have to lean down to change the flap)
remove a stage of flap, check attitude and build speed, start to climb, then progressively remove the additional stages...

yes - don't take it all at once.
richtyler wrote:One quick question when you select the flap position, do you do it in stages or all in one go? I always go stage by stage and as said above select and confirm (either visual or indicated)

In stages. Otherwise you can de-stabilise the aircraft.
With mechanical flaps, you can tell the difference of flap changes by feel and aircraft attitude - I don't do the extra visual checks when in the circuit. I do do the extra checks when on the ground before take off, and normally double check I've removed all the flaps when leaving the circuit (can be easy to leave on one stage in some aircraft - our club Robin has a warning light as a reminder!).
One time during my flight training my instructor deliberately plugged out the fuse for flaps. It gave me a really strange feeling as the plane kept on increasing speed on normal descent attitude and trim after deploying both stages of flaps (It was a Robin HR200). I quickly looked down on the flaps indicator and looked around and found out that the flaps didn't deploy - we did a flapless landing afterwards and this was the experience I would never forget for the rest of my life - I'd look around and check it visually every time I deploy the flaps just as what I would do on the ground.
As riverrock says "all PA 28 s are different.
Prior to getting involved in my current aircraft-PA 28--180C. I used to fly a warrior--very stable-big wing--floats forever.
The 180C doesn"t float--(-only once over hot ground with a temperature of around 30C)
I personally fly wing down to land--straight in -set up, early. Do whatever suits you.
The warrior is a good tourer--it all depends what sort of flying you want to do.