I've now participated in two (count 'em,
two!) successes since the update.
In both cases we failed several times first, but the keys to the wins were organization and planning. The crew does not have to be huge, or super strong. Really, you just need enough staffers to take out the soldiers, and enough people period to fill one side with strong (i.e. maxed Lightning) cannoneers.
Choose who's going to drive before you set out - they should have Take Cover (and know how to use it). Likewise, plan what side(s) you'll be using, and when.
Once on deck and the soldiers are taken care of, "dress the Pearl" (kudos to anyone who gets that), and load your cannon up before moving. Even though you'll get kicked off when the frigates arrive, you'll at least be loaded up, and spread evenly.
When you address the bridges, make sure the best cannoneers are on the proper side. I know nobody likes to sit out, but if you've got someone with super aim and maxed lightning cannonless because the guy with firebrand wants to help...not so good.
Do
not try to rush through the channel. Take each set of bridges out systematically; you won't be able to hit the next set until you're through the previous one, but if you're all in position it shouldn't be too difficult.
When all the bridges are down, wait. Let Take Cover recharge, and just chill for a bit, making sure all your cannoneers are set up and loaded.
When you're good to go, use Ramming Speed and Take Cover immediately after the cutscene. If done right, you really can avoid just about all damage. A full side of powerful cannoneers should be able to take the Goliath down fairly quickly.