Well, they DO sell battery packs, but the wattage that this little thing requires is pretty extreme for those. Also, if you are familiar with the battery units that you can use to jumpstart your car, it is like carrying one of those around. They are also EXPENSIVE.
Here are two that I've found:
https://www.amazon.com/Rockpals-250-Watt-Generator-Rechargeable-Emergency/dp/B075SSMR6K/ref=sr_1_19?ie=UTF8&qid=1527160891&sr=8-19&keywords=battery+pack+with+ac+outlet
https://www.amazon.com/AIVANT-42000mAh-Rechargeable-Cellphone-Appliance/dp/B073GKVNLT/ref=sr_1_20?ie=UTF8&qid=1527160891&sr=8-20&keywords=battery+pack+with+ac+outlet
They are going to eat into your budget pretty harshly.
Now, either of those SHOULD power your system. PC Part Picker claims that the full power draw of the Ryzen 5 2600 system with the P400 (https://fr.pcpartpicker.com/list/7GCwgw) is 152W, which is within the limits of both those battery packs. However, I have no solid idea of what sort of battery life you can expect, but the average laptop battery is 55Wh with a power draw of 90W or so, and that 250W battery pack claims 222Wh, so you can probably get a few hours out of it, even with a monitor.
You really have the most unique build I've ever helped with.
So, I've adjusted your build here (
https://fr.pcpartpicker.com/list/zWph3b ) to help absorb the cost of the battery pack, but without compromising its capability I can't downgrade it any further. You are still going to be over budget with the battery pack.