Hi! If you're looking for a Xiaomi phone under 8k that's suitable for gaming and has a 6000mAh battery, I would suggest the Xiaomi Redmi 9 Power. It has a Qualcomm Snapdragon 662 processor, which is powerful enough to handle most mobile games, and comes with a 6.53-inch Full HD+ display. The phone has a large 6000mAh battery that should last you all day, even with heavy gaming.
In terms of custom ROMs, the Redmi 9 Power has a large development community, so you should be able to find a variety of ROMs to choose from. The phone also has an unlocked bootloader, which makes it easy to root.
One thing to note is that the Redmi 9 Power runs on MIUI 12, which some users find bloated and may impact gaming performance. However, you can always install a custom ROM to optimize the phone's performance and remove any bloatware.
Overall, the Xiaomi Redmi 9 Power is a great value for money and should meet your requirements for gaming, battery life, and customization.