Godox TT685-C (US$110) or V860II-C ($180)? Judge recycle times here.
The V860II-C uses a li-on pack that has the capacity of roughly three sets of 4xAAs. It also slightly speeds up (0.25) the recycle time. But it has no external battery pack port, if you wanted to use a PB960 or something to really push the recycle time. Obviously, at lower power levels, the flashes will recycle more quickly.
If you don't need TTL for on-camera use, you could also go with the single-pin manual flashes, the TT600 or V850II. They're less expensive, but cannot be firmware updated.
All four models have MULTI mode, and do HSS and remote power control as radio slaves. All four models have built-in radio transceivers so they can be used as either slave/master in the Godox 2.4GHz radio triggering system, but only the TTL models can be TTL/HSS radio masters and only the TTL models can be "smart" optical master/slave in Canon's wireless system. All four models also have S1/S2 "dumb" optical slave modes, if you don't have an optical master in the pop-up flash (i.e., using the T6's pop-up). GN is spec'd at 60m @iso 100, 200mm zoom. 360º swivel (vs your Sigma's 270º). M power ratio range is 1-128 in 1/3EV increments (vs. the Sigma's 1-1/16). They also have recycle beep capability to indicate when the flash is ready to fire again.
They don't have great customer support (unless you purchase from Adorama or B&H), but the are part of an integrated lighting system so expansion options are terrific if you go past just using a speedlight on-camera.