Maybe you’ve done it by now, and I’m no expert, but just in case it is helpful: I replaced a linux from a similar dual-boot setup on an old BIOS with MBR, limited to four primary partitions, system this morning. The installer makes it very easy to delete and add whatever partitions you need to. In this case I would first backup your /home somewhere if possible. Then, using the Antergos installer, when you get to the partition tool, I would 1) delete your sda6 root partition. 2) The installer should show empty space there. Click on that space and make a “new” logical partition (your only choice). Select “/” for the mount point of course. I use “/” for the label also. 3) It should offer to make a Grub2 bootloader at sda (the MBR). Even though I had a previous Windows 7 installation with a different bootloader setup, the Antergos installer put a new Grub2 loader complete with the correct Windows entries that works perfectly. The installer should put your Antergos in the new / partition. So I think this will be very easy. In the worst case, if there were problems I think you could delete and remake your same sda4 structure, copying back to /home with your backup. But I don’t think that will be necessary; just replacing the sda6 / partition, putting the new OS in it, and adding your bootloader should work easily with the Antergos installer from my experience.