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An option for you might to consider may be independent travel insurance that also provides for delay of travel and trip interruption. www.insuremytrip.com offers many insurance packages, just compare several to see which package best suits your needs, and contact the prospective insurance company to make sure you understand the coverage.
Having cruised w/ Disney air and without, we have found it to be more economical to purchase airfare and insurance independently while having equal or better coverage.
Disney Magic 1/05 (Eastern)
Carnival Miracle 2/06 (Western)
Disney Magic 12/06 (Western)
Carnival Miracle 10/07 (Southern)
Disney Magic 2/08 (Eastern)
Carnival Freedom 9/09 (Western)
HAL Eurodam 3/10 (Eastern)
HAL Oosterdam 3/11 (Mexico)
HAL Noordam 12/11 (ABC Islands & More)
Disney Fantasy 9/12 (Western)
RCL Allure of the Seas 10/13 (Western)
HAL Nieuw Amesterdam (B2B) 11/14
Be careful of believing that with their insurance, they are 'responsible' for getting you to the ship.
They are not.
When purchasing air through the cruise line they are only an intermediary. They can provide additional assistance in terms of re-working travel arrangements, but there is no magical way for them to guarantee you getting on the ship if there is a problem with the airlines.
The best way to assure yourself of making the trip is flying in the day before. You already mention that isn't possible...so the next best thing is taking the EARLIEST flight of the day to give you as many options as possible for alternate flights if your original flight is canceled or there are delays.
Holland America Westerdam Eastern; March 2015
RCCL Freedom of the Seas Western; March 2014
Holland America Veendam Bermuda: May 2012
Carnival Pride Bahamas: August 2010
RCCL Freedom of the Seas Eastern: November 2008
Premier's Big Red Boat: September, 1989
Carnival Tropicale Mexican Riviera: July 1985