A Simple Kelly Problem I Can't Solve

[Utah]

Here is a Kelly situation I encounter often. I am not sure of the answer and I won't cloud anything up with my logic yet.

In simple terms, I am faced with a max bet that is equal to or below my Kelly value where I can arb the bet with a book that is overfunded (ie, if I don't arb it the money will go unused in the second book). Intuitively, the problem seems incredibly easy - you are below Kelly and any arbing has negative expectation. Don't arb. But, by some twisted logic and math I can make a strong case for arbing a portion of the bet.

Do I arb here? Is there ever a case where you arb when the soft side is below Kelly value?

Book A: overfunded
Book B: Overfunded

Arb: Book A: +104 Book B: +100 (book B is soft)
Non-vig line approx -108
Softline value = 4.2%
Chance of win = 48%
Value of arb = 1%
My basic Kelly calculator says bet $1000
Max Limit For Bet for Book B = $1000

I bet the $1000 max at Book B. Do I arb any portion of the bet with Book A?

note: I am very ill and not thinking 100% clearly. So, this may be a very easy problem. But, I don't think so.