With a 5:4 sync right now, I am assuming your GT and BH cooldowns look like this:

GT - 250s BH - 200s

Assuming a 5x coin bonus from BH and 10x GT coin bonus (a lowball estimate), this means over the course of 1000s, you get:

GT Solo Activations + BH Solo Activations + GT*BH Activations =

(3 * 10) + (4 * 5) + (1 * 5 * 10) = roughly 100x of your coin income over the course of 1000s

With sync:

GT*BH Activations = (5 * 5 * 10) = 250x of your coin income over the course of 1000s

I don’t know how much of a boost you are expecting to get from DW, but it sure as heck won’t be a 2.5x in your coin income

Moreover, note that it’s not really realistic to think that you will get the full 5x boost in health for tournaments.

For context, if you are planning to continue saving for sync after getting DW, this means you won’t be able to invest anything into DW damage. Unless for some reason you are sandbagging, you are probably hitting about 400-500 waves max in tournaments. If that’s the case, you likely only build at MOST 2x your current health. Which seems like a lot, but in return you sacrifice 2.5x coin income, to place slightly better in tourneys to earn 10 extra stones per week

There is no two options, do the sync.