First off...make sure you have your ADRs ranked in order of difficulty when it comes to booking. Obviously, 'Ohana dinner is a tough one, but it may not be as hard if the meal falls later in your trip. I think Chef Mickey's breakfast will likely be your next most difficult, but Cali Grill timed with Wishes won't be far behind. Narcoosee's and 1900 PF always seem to be be easier to book. In fact, I switched things around last minute last trip and got a decently timed dinner at Narcoosee's the day before...although, last minute openings seems to be the new way to stalk the site since so many people drop last minute to avoid no show fees.
Beyond this, I much prefer the website over the phone. I'm not saying it's perfect, but I find it much quicker and adaptable/flexible than the phone. I'm to the point that I'll have my laptop going as well as DH's when I book ADRs. This way, while one is 'thinking' - I can get the ball rolling for the next ADR on his. I've done test runs with this method and while it's kind of insane, it's shaved about 5 - 7 min off of my overall ADR booking time on day 180. I also have our phones and tablets ready to go in case the website jams but the app is working. Plus, the website opens an hour before the phones, so it only makes sense to try online before resorting to calling. A few other tips---> start trying just before 6am ET since sometimes the website flips early...try searching dinner vs. a time if you're afraid slots are going to be in high demand...if something isn't showing openings right at 6am- try again in a few min after booking something else - as all time slots aren't always loaded to the website right at 6am.
As for suggestions in case you can't get any of these...Citrico's is another great option in the MK area. We're also big fans of Yachtsman and Flying Fish if you're over in the Epcot area. Sanaa and Jiko would be great choices if you're willing to head out to AKL. Not sure if there's a really good substitute if you can't get 'Ohana, but other fun meals are WCC and 50s. As for character meals, like I said- don't see 1900 being an issue...I mean, I booked it for my bday around the 150 day mark and there were TONS of openings. In fact, I had lots of Chef Mickey's openings as an option too.