Battery recommendation

Let me see if I understand this correctly. The maximum current draw of that the lights I ordered is:

Conway S2+ 8x7135 drivers= 8x350= 2.8A
AstroLux S1 (on turbo): 5.9A
S41 (on turbo): 7.6a and up to 11A and beyond?

The Conway is fully regulated so any battery that can deliver 2.8A (and they all should be capable of doing that) should do, right?

The S1 and S41 on turbo however are basically unregulated directly drive. The 219BT (not sure if that is the correct one) datasheet specifies an Absolute Maximum Rating forward current of 1500mA so with 4 of those the permissible tail currrent for the S41 would be 6A? So if you put it on turbo with a 18650 Samsung 30Q IMR you would be frying the poor things?

The Cree XP-L datasheet specifies a Maximum Drive Current of 3000mA so again at 5.9A you would be frying it?

Am I missing something here? Should I be looking for batteries that max out at 6A for the S41 and 3A for the S1 to ensure emitter longevity?