I am not an expert on silver cells, but the one thing I can assure you, you're going to need a massively more powerful power supply, much, much bigger. 1 amp is nothing, the scale of what you are projecting is more like 20 amps, though I guess you could run the thing for weeks...but I can only assume you are operating on this larger scale in order to handle larger anodes and larger deposition rates, and for that you will need LOTS more power. (There are calculations for this available on the forum which I am not doing here, I am only eyeballing your proposed setup) It's like you have a Chevy and are proposing to put a lawn mower engine it.
I will admit I am confused as to your power source. It says "1 amp" but the dial goes up to 12.5 (which could certainly get you going) And it's made by "Esso" an obviously automotive battery charger but then why would it say "1 amp"? If that source goers to 12.5 amps, that could work for you.
Secondly, I would imagine that if your anode basket is only a little smaller than your overall container, as it appears from your pix, your anode of course is going to sit at the bottom of that container and will thus be very close to your cathode. I'd therefore imagine that you would be in greater danger of having the crystal growth on the cathode grow to where it shorts out to the anode much quicker than would occur if you have a smaller anode basket. The cells I have seen posted have a much smaller anode basket than what you are proposing.