The pistons are a disposable item.
https://www.sngbarratt.com/English/#/UK ... 0piston%60
You seem to have S2 front calipers. So something like this is what you need
https://www.ebay.com.au/itm/28516559708 ... BMgoqH2sti
Looks like Moss USA have them too and also have the channel seals
https://mossmotors.com/xke-7827-front-b ... ser-ii-iii
Clean the housings, new kits and pistons and you're good to go.
Don't forget to replace the small channel seals between the caliper halves; you may need to go to a specialist brake place for these.
Check torque value for the joining bolts, scrupulously clean the threads and assemble dry.
For future reference, to remove pistons don't disassemble the caliper halves. Slide a piece of wood approximately the thickness of the disc inside the caliper between the pistons. Block all but one of the hydraulic fluid holes, then cautiously blow compressed air into the caliper.
Silicone vs mineral fluid is an endless argument on fora. To change you'd need to get all of the mineral fluid out of your system which isn't necessarily easy. I'd stick with what you have.
Caveat. If you are not 100% confident and experienced working on brake systems, get your local brake place to do this for you. It'll cost you double what the kit costs but brakes are mission critical and you really don't want to crash in a 60 year old car.