Am I getting something wrong? (Selling ITM puts against my shares for premium)

I own 100 shares of FPI @ 13.38 per share. I am over bag holding and want to get rid of these shares. FPI is currently trading at 9.72.

If I sell the shares straight up it is a $972-1338 = -$366 loss.

Currently I can sell a put against my 100 shares for $14.50.

$1450 – 1338 = $112 gain.

Should I sell a deep ITM put against my shares with the assumption I am getting assigned? I want to get rid of them anyways.

Is my logic flawed?

Thanks.