FYI, the weather has been cool and rainy the past couple of weeks so you may have a bit longer road walk than I initially suggested. Still doable, and as long as it doesn't get really hot right before or during your climb, avy conditions should be ok, however, you are right to be concerned. This time of year 'climax' avalanches can occur, which is basically a giant slab avalanche down to the ground or glacier. The Coleman-Demming route gets as steep as 30 degrees on the Roman Wall, the very bottom end of the most likely avalanche terrain.
Mt. Baker is my favorite volcano in the Cascades. I've guided, climbed, and skied it over 30 times by eight different routes. If Baker doesn't work out because of the weather, I highly recommend the Stuart Range for better rather than the Olympics. Really much better mountains with a much shorter drive (especially if you drive around the south end of the Puget Sound) and no ferry necessary (provides a more direct approach from Seattle, but kind of a hassle and not especially inexpensive), although a ferry ride from Seattle to the Olympic Peninsula is a classic Seattle tourist experience. Take a look at the following:
Dragontail Peak: NE Couloir would be a pretty strong mixed climb, and likely in shape, expect technical ice and mixed/rock climbing. Triple Couloirs may or may not be in condition, I've not heard of anyone climbing it this season, but there is latitude on the route if the crux ice runnels are not in shape. A bit easier than the NE Couloir, or harder depending upon the exact route variation and condition, expect technical ice and mixed/rock climbing. These are the most difficult routes that I will suggest.
Colchuck Peak: NE Couloir or North Buttress Couloirs would be good, moderately technical climbs. Easier than the routes I mentioned on Dragontail, but right next door. The Colchuck Lake cirque has been called the most beautiful spot in the Cascades by one of my partners, who is a professional photographer.
Argonaut Peak: NE Couloir, moderately steep climb, may involve some rock climbing, but sports a really cool ridge traverse and 'tunnel' right before the true summit. This is the least commonly climbed peak that I will suggest. Two friends and I made the first winter ascent and one partner made the first ski descent in February many years ago.
Mt. Stuart: Sherpa Glacier, steep snow climb to a classic summit. Ice Cliff Glacier, steeper snow climb, maybe some ice and rock, somewhat dangerous, numerous accidents (including your's truly) and at least one fatality. Stuart Glacier Couloir, my personal favorite route on Stuart for this time of year, offers a steep ice/snow couloir topping out at the beginning of the technical portion of the West Ridge, rock climbing at 5.6, but variations can be done making it more difficult. I found it plenty challenging with crampons and ice/snow covering the rock. I had previously soloed the West Ridge in a day wearing running shoes and found it much more challenging as a mixed climb. Mt Stuart is one of the 50 Classic Climbs in N.A. (the upper North Ridge), and the north face routes I mentioned involve as much elevation gain as the Grand Teton with the same vertical relief as it's north face.
Most of these peaks have non technical routes to the summit and can be done with a single ice axe and crampons. Dragontail via Aasgaud Pass, Colchuck Peak via Colchuck Glacier, Mt. Stuart via Sherpa Glacier from the north. If the approach to the south is open then the Cascadian Couloir would be the easiest rout to the summit, but I don't recommend it. If approaching from the south, here is a fun outing:
http://www.summitpost.org/mt-stuart-west-ridge/517399.
Any one of these routes would be, IMNSHO, better than anything in the Olympics you might find. Many are 'bigger' ticks compared with the Coleman-Demming route on Baker. Their position east of the crest gives you better chances of good weather. I don't think you would be disappointed at all if you managed an ascent of any of these routes and peaks. I suggest just be open to other possibilities and bring enough gear (ice tools, rock protection, ice screws) so you are not limited by technical difficulties.