We've not been all the way up Burke or Dean inlets to Bella Coola, but have "Crossed the Queen" (that's Queen Charlotte Sound, rounding Cape Caution between the Broughtons or Vancouver Island and the BC central/north coast) many times.
Here's a bit from our book:
Crossing the Queen
Beyond the more protected environment east of Vancouver Island, “Crossing the Queen” (Queen Charlotte Sound) to the BC North Coast represents a significant milestone for many cruisers. This open water crossing including some 30-40 exposed miles can provide a real challenge in winds and seas. It can be rather long but no big deal, or in the wrong combination of wind and tidal currents it can become a small boat’s worst nightmare.
Obviously you wouldn’t want to be out there in strong winds, but there’s more to the analysis than just wind speed. In our experience, one combination to be avoided is a strong ebb current flowing west with westerly winds greater than 12-15 knots. Similarly, a flood current with a southeast wind might not be a good choice. Small aluminum mail boats cross the Queen regularly, and they tell us that even 20 knot winds can be no great challenge, if not opposed to current. I’d stick with a max of 15. BC’s VHF marine weather gives actual conditions at key points, like Pine Island and Egg Island, which can really help you decide when to go.
In ”normal” weather, with wind primarily from the NW, calmer in the morning and building in the afternoon, a fast boat with an early start can avoid much of the challenge. But crossing at slow speeds you’ll be out there for quite a while, and you’ll want to pay careful attention to tides and weather. You don’t have to run all the way from Port McNeill or Port Hardy up to Rivers Inlet in one fell swoop. There are protected anchorages at Blunden Harbour, and closer to Cape Caution at Miles Inlet, Skull Cove, and others near Nakwakto Rapids.
There’s a special situation along the way you certainly want to avoid: wind from the west at the same time as a strong ebb current through the Nakwakto Rapids, flowing huge quantities of water from Seymour and Belize Inlets out through the narrow Slingsby Channel. This can set up a train of large and steep waves, starting in the mouth of Slingsby and continuing on westward for a mile or more in the open ocean. Check the Nakwakto current tables to see if this combination is likely, and if so steer clear, further out west than you might otherwise.