Congrats, I am jealous beyond belief; I have always lusted after a beautiful colour-phase bear like those. The bear in the last pics is magnificent.
As far as squaring and scoring and all the other measurement-taking...sure, do it if it floats your boat, but does it really matter? You have the experience of a terrific hunt, and the memory of the event will be heightened each time you look at the trophy. Will a number (of inches, or pounds, or whatever...) really do anything to improve that? I've never "scored" an animal in my life and somehow it hasn't caused me any grief.
What are you planning for the hide? Traditional rug, full mount, or...?
Be careful when you do the skull. Dish soap is indeed a great way to cut the grease, and bear skulls are notoriously greasy. If it dries and starts to show yellowish areas, there's still some grease there and it needs more simmering in the soap solution. Be very careful when dumping out the water, as the teeth will loosen and it is easy to lose some of the smaller ones. Finally, when the skull is clean and dry and white, a few coats of watered-down white glue painted on will strengthen it and reinforce the bone without looking artificially shiny. I hope you post some pics of the finished product(s).
Again, congratulations!