Summary - Hiking Three Corner Rock and Birkenfeld together combines good views, no views, an open summit, a forested summit, a long hike, a stiff bushwhack and decent elevation gain. You can do this TRC first or Birkenfeld first. Starting at the Rock Creek Pass trailhead (45.74910, -122.04310) follow the PCT east to (45.71410, -122.00700). From here you have a short steep bushwhack up the ridge to the summit of Birkenfeld. Come back down the same way and return to the way you came, turning off the PCT to the Three Corners Rock trail. The TRC hike is easy and ends in an large open summit with great views on a clear day. Get your QSOs, head back down to the PCT for the hike back to your car. You'll cover roughly eleven miles with 2600 feet of elevation gain on the round trip. You'll probably see people on Three Corner Rock and have the PCT to Birkenfeld to yourself.
TL;DR - Having ticked more than 100 LC summits in the last couple of years, I've been on top of the almost all of the easy-to-reach hills that are also close-to-portland. And being easily bored, I am not often interested in repeating hikes even if they don't require hours on the road, so I spend a lot of time pondering sotl.as and USFS maps, looking for new routes and summit combinations. This is one of those...
Most people hike to TRC from the Rock Creek Trailhead or the Three Corner Rock Trailhead (see this entry on TRC) and Birkenfeld as a short heinous bushwhack from the east (see my post on Birkenfeld), often in combination with Greenleaf Peak (W7W/LC-104). I wasn't much interested in doing Birkenfeld from that direction again but linking it with Three Corner Rock via the PCT looked like a good route that hadn't been tried before.
You can read my post on Three Corner Rock for directions to the trailhead and other info. For this hike, I did Birkenfeld first, wanting to save the TRC view for later in the day but you can do the hills in either order. The hike from the trailhead to the Birkenfeld summit bushwhack covers five miles and roughly 1600 feet of elevation gain, with most of that in the last mile of the hike. When you get to lat long (45.71410, -122.00700) start looking for a way up. You'll want to follow the ridge going northeast, which is steep but easier than the usual route from the east side. When you've finished, return the way you've come, hiking along the PCT until the turnoff for Three Corner Rock at lat long (45.73646, -122.04318). The half mile hike will feel pretty easy after all you've alread done!
This turned out to be a good combination of hills with the bonus that the Birkenfeld summit climb is a lot easier from this side (though still steep with a bit of brush bashing). The Pacific Crest Trail makes for a good hike and there is enough up and down to keep it interesting. Finishing with TRC is recommended; it is an easy hike and the views on a clear day are terrific.