We've done Cape May a bunch of times and really like it. It is probably our favorite breakfast TS, with 'Ohana a very, very close second.
To get from the WL to Cape May, the easiest (but most expensive) way would be to take a taxi. You can also boat to the MK and then transfer to a Beach Club bus, or bus to the MK and transfer to a Beach Club bus. I'd estimate 45 min to 1 hour of travel time each way for the bus/boat options, and 15-30 minutes each way for the taxi, depending on wait times for each leg of transportation.
Have you considered going back to 'Ohana...the dinner experience and the breakfast experience are very different. I wondered the same thing on one of our past vacations, too...back-to-back 'Ohana ADRs...but it worked out great. I didn't think I'd like the breakfast served family-style, but I really did. And the character interaction was terrific!
IMHO, it is not worth all the travel time and hassle to go to the Beach Club just for a meal when 'Ohana and Kona are right there. It is going to be hard to get packed up, get to and from breakfast all the way over at the BC, and be ready for a 12:00 DME pick-up. Going to the Poly may give you more time to relax, get breakfast, take some last pictures, do a little shopping, etc.
Have you considered going to Whispering Canyon in the WL?? That would be a GREAT time and sanity saver! I've never been to WC, but when we were staying at the WL I wished I had booked an ADR. Every time I walked by, it seemed like everyone was having a lot of fun.