BUT WAIT! There's more!

So, Bartering also says you'll earn 10% more when you sell items. So, I assume that Influence will work the same way. So, my Lohse should get 32.5% more based on the base value.

V = base Value
I = bartering Increase (10% represented as 0.1 as it would be)
S = value as Sold to vendor

So, without any bartering or influence, you divide the base value by 2.5 to get the sell value. Given that we now know that bartering applies to the base value and not the adjusted value, we can determine that, on the same 60-value item, I should get a 19.5 gold increase when selling the item back to the vendor.

60 / 2.5 = 24
And that's indeed what I'm seeing on Sebille.

So, inverting our prior equation of (V * 2.5) - (V * R), we get (V / 2.5) + (V * R), or:
(60 / 2.5) + (60 * 0.325) = 43.5
And that's what I'm seeing on.... nobody...

OK, so Lohse, who should be seeing a 32.5% increase, is seeing a sell price of 28.

If I divide 0.325 by 2.5 and then multiply that by 24, I get 3.12. 24 + 3.12 = 27.12, and if we round that up we get 28. I guess it only rounds up, because I can't get 28 as a result any other way.

So, the calculation is:
(V / 2.5) * (1 + R / 2.5)

So, no matter how you cut it, we're not getting the bartering increase when selling to vendors. There's just no way to look at it where we do. At least if my 32.5% increase got me to 31.8 gold (24 * 1.325), I'd understand (although it still wouldn't jive with the way the vendor's sale price is calculated), but actually reducing the percentage and then applying it to the already reduced value? I don't get it.