You might consider applying for the Platinum Card from American Express (not the DL co-branded one). You will get Skyclub access with a same day DL boarding pass (and discounted entry for a guest). It also gives access to a few other lounges through free membership in the Priority Pass Select program. Also gives SPG Gold status and Hertz Gold status (nice perks if traveling a lot and using those programs).

It's a $450 annual fee which is steep, but there is a $200 airline fee reimbursement. So if you have checked bags, economy comfort seat purchases, in flight food/drink purchases, etc those will be reimbursed when charged to the card. Also gives free Global Entry, normally $100.

So if you were going to pay $100 for 4 day passes, you could instead get this card and pay $450 for a full year of Skyclub access. Then the cost gets offset by the $200 fee reimbursement. The sign up bonus points would more than cover the $150 left that you end up paying out of pocket.