I just noticed the petrol gasket maybe be worn out its leaking on the top cover of the carby, looks wet around it.

either fix that or time for the 32/36 weber!

Lets think about it.........................Webber

I say go with the webber as well!!!!

What do you actually need to put a webber on an A12 (other than deep pockets for fuel lol)

I had the same problem with my auto 120y, it would drive fine but as i reduced my speed to stop it would want to die. It would idle at about 700-900 so i would be forced to come to a stop gradually and click it into neutral. I found that this was exemplified when the engine was still cold or the weather was quite hot.
I serviced the car and adjusted the idle and mixture. I also started running the car on bp ultimate and found it to be much better. I found that mine had to idle at about 1200+ in neutral for it to be reasonable when coming to a stop. I found that my carb was flooding when coming back to idle from acceleration.

Have a look at freeing up a bit of power at low rpm by changing over to an electric fan.

I was able to get my stock carb running well enough but decided to change over to a weber 32/36 DGV. After some initial idle and fuel mixture problem i have been pretty happy with how it has worked. Be aware that it will definitely take a lot of playing with before you'll be happy with it.
In all seriousness i'd keep the Hitachi as its the most economic and smooth running carb you can use.
Just take the carb to a reputable carburetor specialist and get it rebuilt as that