The question asked
The question asks how to slow down the epoxy setting, and the reason is because the process you're using doesn't leave enough working time to glue multiple pieces, wasting a lot of materials. You've already identified cooling as a way to slow it down (probably the easiest way, although that won't buy you much time).
To answer the question you asked, the setting time is driven by the chemistry, so the ideal solution for gaining more working time is to use an epoxy system designed for a slower setting time. Once you select an epoxy system, I'm not aware of a good way to change its speed through chemistry (at least not with anything you would have at home). You especially don't want to reduce the hardener. That won't slow it down, it will just leave unreacted resin in the hardened mix.
Using a slower-setting epoxy or cooling the one you have would be the best solution for slowing the setting speed. However, slowing the setting speed isn't the best solution for your problem. The problem is really the process you're using.
Better solution to the problem
It sounds like two issues are driving the desire for more working time: blending and using the mica mixture to glue the parts, and lack of a good way to mix smaller batches, resulting in wastage if you don't try to glue multiple pieces to use it up.
Mixing the mica into the epoxy used to glue the pieces is a bad idea. It's not just using up some of the working time and complicating the glue-up, it's also affecting the alignment of the pieces.
Pieces of broken porcelain typical fit back together with zero gaps. Anything you put between the pieces will prevent a perfect reassembly. Each glue joint will throw the remaining pieces farther out of alignment. Adding the mica to the epoxy introduces solid material between the porcelain pieces that will prevent them from fitting back together perfectly.
Possible alternate assembly adhesive
For comparison, low viscosity superglue (cyanoacrylate) is probably the best adhesive for porcelain repair from the standpoint of pieces fitting back together. It works with a microscopic layer of glue, so pieces fit as perfectly as they're going to get. Unfortunately, superglue is very brittle, and even the waterproof ones won't handle water immersion if the tea set was to be used after repair. They also don't handle heat well.
If the tea set will only be displayed, you could use superglue to reassemble the pieces, then reinforce that with epoxy over the seams so it still looks like kintsugi. That's also the fastest way to repair it since there is virtually no curing time during assembly, especially if you use an accelerator. Just an alternative approach to consider.
Plain epoxy for assembly
But back to doing the repair entirely with epoxy, using just the epoxy without the mica to reassemble the pieces will let you compress the seams more for a better fit. Slowing the setting time will work against you. You will achieve the best fit by assembling several pieces to verify the alignment, then gluing just the piece most critical to aligning the other pieces. Use the least amount of epoxy that will hold the pieces together without excess, and squeeze the pieces together to spread the epoxy into the thinnest layer possible. If you can, use tape on the seam to stabilize the joint and keep a little compression on the seam. Let that do its initial cure, then repeat the process with the next piece. Slowing down the setting time will stretch the time needed for the repair.
The objective should be the best possible repair on the tea set. That will take as much epoxy as it takes, just don't unnecessarily waste it. Don't jeopardize the repair and the tea set to save a little epoxy. If the pieces interlock enough to stay together, you can try gluing more than one piece at a time, which will make better use of the epoxy. Without the mica at this stage, you're only wasting epoxy, not the mica, too. A faster setting time will reduce the chance of the parts moving during the cure.
Once the pieces have been reassembled, the surface isn't likely to be perfect. There will be missing chips of porcelain, surface gaps where the epoxy didn't fill the whole seam, etc. Use the kintsugi for that. Mix an undersized batch of epoxy plus mica, and use a syringe or similar tool to paint it precisely along the seams. If you run out, add a little more. For this stage, you can make a batch big enough for the whole object (or as much of it as you can paint in the working time), and cooling the mixture to stretch your time will be beneficial. Use a disposable syringe since it won't be worth trying to clean it.
You might even want to use a fast-setting epoxy for the reassembly, and a slower-setting epoxy for the kintsugi.