How should I spend my stones?

Right now I have two choices:

Spend 680 stones for GT/BH sync.
Spend 800 stones for DW.

I'm low plat so my current weekly income is 145 stones. So the minimum time I need to spend to get the second option would be around 4-5 weeks.
The benefits for each would be:

  1. DW:
    1. More consistent high-tier farming: Right now I'm trying to get DW as a free UW to farm higher tiers. Also, the health increase would be better than one that comes with the free DW
    2. More coins: Since I'll be farming higher tiers for longer, my coin income will increase. Another small increase would come from the death wave coin bonus labs.
    3. More lab cells: Longer high-tier farm -> more cells. Another small increase would come from the death wave cell bonus labs. (but not much since my coin income is not high enough yet to research many levels)
    4. Better tournament performance: I'd have 5x health in tournaments as soon as I get DW and within a week I estimate to raise this to around 7x (and it will get better the more time goes by). I could probably earn 10-20 more stones per week due to better platinum placements.
  2. GT/BH:
    1. Coin increase: I currently have a 5:4 sync, my BH earns approximately 10% of my coin income and my GT earns approximately 50% of my coin income. So I estimate that a 1:1 sync would give me an extra 4x of my BH income and since my GT cooldown will be faster, I estimate a 25% increase in the GT income. That would mean 100%+4x10%+0.25x50% ~= 160% coin income. I'm not 100% sure about these calculations, someone told me that both GT and BH count the income from syncs so by increasing the BH income by 400%, I should be including the whole benefit of the sync.
    2. Cash increase: I'd earn 25% more cash from GT in tournaments because of the reduced cooldown so I expect a slight improvement.

https://preview.redd.it/zw5uirnisf0e1.png?width=863&format=png&auto=webp&s=55543b4eece300c7265a262c00fd42f2f0fceb4d