Hi Chris
I use dot 4 synthetic as well. However, I would suggest you do flush all the old fluid right out of the system first, I did this with an old reservoir cap and fitted a tyre valve then used a foot pump to purge it all out, open all the bleed valves and use some small rubber hose into jars. Refill with new fluid and I did it once more with the new fluid to make sure all the old fluid had been washed through, it does waste that much fluid, then I refilled it with the bleed valves open to make sur the fluid started to run through and my able assistant watching we tightened the bleed vales topped up and bled the system in the normal way.
Hope that makes sense.
I will be doing the same again soon, once my engine is back in car.
Good luck
G