If you remove your 2x 120mm front intake fans and leave only your 1x 140mm top exhaust and 1x 120mm rear exhaust fans running then you'll cut your case cooling performance in half.
Currently, you have a little bit of negative pressure inside your case since your exhaust fans remove a bit more air than your intake fans can draw it in. Without any intake fans at all, you'll be left with strong negative pressure. While on cooling standpoint, and in high heat production rigs, the negative pressure is better, it also comes with a big drawback. With strong negative pressure, your case draws the needed air in through every gap, nook and mesh, which in turn causes more dust to enter your system. Since you have a lot of mesh paneling, i don't think you can filter them all to prevent dust entering your system.
Without knowing which MoBo you have and how many fan headers your MoBo has, the best option for you would be to buy a fan controller that you can mount into one of the three 5.25" external bays in your case. Here are 4 LED touchscreen fan controllers you can go with,
pcpp: https://pcpartpicker.com/products/compare/FTXfrH,dQ8Zxr,9f6BD3,XnnG3C/
All 4 fan controllers support up to 5 fans that you can control manually via touchscreen, according to your needs. I added the Bitfenix Recon if your case is the white one for better match to your case.
With 5 channel fan controller, you can add your bottom intake fan as well, for creating positive pressure.
If you don't like LED touch screens then you can go for a fan controller that has buttons/sliders for fan controls,
pcpp: https://pcpartpicker.com/products/compare/YD4NnQ,qnQRsY,tWW9TW/
Or if you prefer LED screen and buttons as well then you can go for the same fan controller that i'm using in my Skylake build (full specs in my sig), a Thermaltake Commander F6 RGB,
specs:
http://www.thermaltake.com/products-model.aspx?id=C_00002777
newegg:
https://www.newegg.com/Product/Product.aspx?Item=N82E16811998156
amazon:
https://www.amazon.com/Thermaltake-COMMANDER-Channel-Controller-AC-024-BN1NAN-A1/dp/B01B9618C2
Here are also few pics of my fan controller,
link:
http://www.tomshardware.co.uk/forum/id-3272328/show-newest-system-upgrade-components/page-5.html#19565270
NZXT Sentry Mix 2 and Thermaltake Commander F6 RGB both have 6 channels for 6 fans. I'm not sure if you can mount 6th fan as side intake or not. But with Thermaltake Commander F6 RGB, you can use the 6th channel for connecting the Thermaltake Lumi color LED strip, since fan controller comes with 2x adapters for LED strips,
specs:
http://www.thermaltake.com/accessory.aspx