There are 2 factors that might dictate your trail/mileage: (1) ONP is very large, so a loop is probably your best option, unless you have a definite shuttle worked out ahead of time. It's still 2-3 hours back to SeaTac even from the Hood Canal side. (2) It's a NP, so you have to camp in established campsites.
Here's a loop that I like:
Start on the east side/Hood Canal side near the town of Brinnon. The Dosewallips River Road is washed out about 4+ miles up, where you leave the car. You can hike up the road to the Dosewallips Campground/TH, where the trail starts (this is uphill but easy walking that could be done with a late start). Then following the West Fork of the Dosewallips River up to Honeymoon Meadow, up and over La Crosse Pass to the Duckabush River, up to Marmot Lake/Hart Lake, over O'Neill Pass and around to the Enchanted Valley. Here, it might be fun to walk down the valley a few miles to the ranger station, then back up and over Anderson Pass, with a side trip to Anderson Glacier. Over Anderson Pass and you're back to Honeymoon Meadows and down the road to the car. you shouldn't need any crampons/axes, as this is all hiking. Also, the distances don't seem that great, but sometimes the trail runs through thick forests with lots of downed trees and has a few stream crossings.
The last time I did this (2003?), I carried a heavier load, probably 40+ lbs. We camped at Dosewallips TH, Honeymoon Mdws, Upper Duckabush, Hart Lake (a short day), Honeymoon Mdws (this was a long day) and then out. You should be able to manage the distances better with less weight. That trip we saw 9 black bears and a herd of Roosevelt Elk.
Here's a shot of Anderson Glacier, sometime after O'Neill Pass: