Given specific equipment wattage, and the capacity of an industrial grade portable battery, how can I determine theoretical run time?
which has a reported 400 watt-hours of capacity That basically says it all.

It can deliver 400 Watt for one hour or 40 Watt for 10 hours or 80 Watt for 5 hours. See how the Watts and the hours multiplied always result in 400 Whr ?

Next step is to detemine how much power your equipment actually uses. Those PEAK numbers are as it says: peak values. If you have a Power meter like this:



You could just measure the power consumption.

Then there's the conversion losses (efficiency) of the portable power pack, some energy is lost between the battery and the outlet on the device. Assuming it's a good design a safe bet would be 80 % efficiency (I just sucked that value out of my thumb so use a more accurate value if you have that).

That means you cannot actually use 400 Whr but you only get 80 % of that which is 320 Whr.

That 1.4 A of the Pioneer RMX-1000 unit is actually at 5 V. This device actually consumes very little power. If we assume 15 W max for this unit that would be a conservative guess.

Peak values are not what a device consumes on average over a long time, I would take half that value in case I was unable to measure it. So I estimate your setup's total power consumption at 2 x 10 + 15 + 10 W = 45 W

so with 320 Whr that would be 320 / 45 = 7 hours.

That's my rough estimate, no guarantees !

But I see no power amplifier to drive the speakers. If you forgot those that might have a big impact on the runtime as power amplifiers are often power hungry devices (and if it is one which gets warm/hot even more so).

BTW that portable power pack is not and does not look like what I would call "Industial grade", at USD 500 it is definately a consumer device. I would expect a similar device for professional use to cost at least 4x as much. But if treated carefully, this Anker power pack will do the job, no need to spend more.