I want to give an update on this. as I promised when I started this thread.
First I did make a mistake, I thought 2 4awg wires = 1 2awg wire. I probably got this wrong idea from nail gauges, for which the width is what matters, but for wires, it's the area and 2 4awg wires are equivalent to a single 1awg wire. (My renogy inverter comes with 3 feet cable which is made of 2 4awg wires in parallel)
As I was building the battery, I also found a space in my trailer, under the microwave cabinet, that would fit my 2000w inverter, this cuts the distance I need to run wires by more than half and I was able to avoid some very sharp turns. so I ended up using both 2/0 awg and 1awg (not 1/0) wires between battery cell and inverter (~1 foot 1awg, ~5 feet 2/0).
I tested the setup at ~180A for over 15minutes(A 13500BTU A/C, and a hair dryer with heating turned off), with a temp gun scanning varies components between cell and inverter.
Almost everything remained cold (< 2 degree higher), with the exception of a 250A manual reset breaker, which got fairly hot. Later I read these kinds of breakers are supposed to get hot to do there job(thermal breaker)
I hope this will help other people in similar situation.
Also thanks to all the folks responded to this post with fact, data instead of strong opinions.