I used to fly an executive jet and we had the same problem with the final part of the landing. Not sure the same thing would apply to your larger aircraft but this is how we dealt with it.
If one flared a little too much there would be a firm touchdown. This was because of the swept wing and the main wheels being fairly far back.
So near the ground that final touch of flare would raise the nose but at the same time lower the main wheels firmly onto the ground.
The answer was to check slightly forward instead of persevering with the flare. This would reduce lift, whilst slightly lowering the nose but at the same time “raise” the main wheels and stop them descending firmly onto the ground.
Whether the same applies to your Airbus or not I don’t know!
That's where there is a subtlety.
Actually, pushing down increases lift. At first.
First, it increases lift on the tailplane.
Then, the airplane tilts down.
Then, lift decreases.
However, if you push a little bit very late, the combined effect of the increased lift and the wheels raising will be able, sometimes, if done right and with a bit of luck, to make for an extra smooth landing.
However I would not recommend this technique. It will only work if the airplane is already very close to the ground.
The best technique I found is to flare at the correct height. 40ft is definetely too high except maybe for a high slope on 321.
Real flare height should be 20ft for 320/319 if done with a "rather high" pitch up rate.
Flare height of 30ft corresponds to a smaller pitch rate, one that I personally do not like so much.
So, given the fact that you like to flare high, I would advise you to flare very slowly at first just to reassure you, but to perform the real flare later. For example you could slow the descent from a 3° angle to a 2° angle very progressively from 35/30ft to 20, then flare for real at 20ft, but still a gentle flare since your slope would be reduced.