Jesse, I dunno exactly where that wall is. I do know that wand solution size and valve play a limiting factor, they are just as important as jet orifice size. That is why you won't see many jumping to 3/8" solution line for carpet cleaning, lots of other restrictions to overcome first.
A standard Greenhorn wand puts out more water than a steamway wand with factory jetting on 1/4" line, so it would make sense to fix the wand plumbing and jets before upgrading to 3/8" line.
3/8" line can "potentially" deliver twice the water volume of 1/4" line, and that can preserve the core temp of the solution, but ain't much going to be noticed if your wand plumbing and jetting is undersized, plus most 3/8" lines are steel braided, they radiate a lot more heat, read this as "lose heat" on a 200' hose run.
And yes there are thermoplastic hoses avail. in 3/8".
I agree with Larry on moving the water and the BTU transfer, but i disagree with: " The concern I have is wicking of stains from increased levels of water. "
Why would they wick Larry?
I assume you are inferring they are "wetter" by some degree?
I say they stand a greater chance of being "net drier".
Even if we could theoretically extract 99% of what we put down, we would still leave 1%.
Based upon that 1% theory, one super flushing pass will only have the water in the carpet/stain for a fraction of a second before it's extracted, leaving the carpet incredibly dry.
The same is not true with repeat rinsing passes of a lower flow rate that leave 1% each time, 1% that we will never extract, each subsequent pass leaves a cumulative residual moisture.
Even if it only takes two light rinsing passes to equal the cleaning of one super pass, the carpet would still be considered "twice" as wet and require twice as long to dry.