Unless the team promises to relegate Saunders to a bench role I'm not sure I can see them being able to convince Jackson to sign here. From his perspective, he wants to increase his value for the contract after this one so taking a PT role defeats that purpose. I imagine he probably said something similar to the Angels, though the one-year contract they offered probably wasn't all that attractive either.
OTOH, it'd be a guaranteed $15M for him (if we go by your offer). Not bad considering his abilities haven't been at their peak lately.