There’s nothing remote about camping on baker lake. There are two campsites on the east side of the lake you can hike to, one from the south end, and one from the north end. Boaters camp in these areas too, so don’t be surprised if there’s a big party next to you. The view though……. Might be worth any inconvenience.
There is a trail up the river to a campsite, sulphide creek. Depending on your definition of remote, you might try Shuksan Lake, or Marten Lake on Lava Divide. There’s going to be a ton of snow in those areas that will stick around into August.