We did most of your route in 2008
https://www.crazyguyonabike.com/doc/..._id=96161&v=I9
There were some very steep climbs at some points and these may be difficult for a tandem. Especially the climb after crossing the lake from Rapperswill - the initial climb on sealed road is challenging but it gets steeper when you turn off onto gravel roads. After crossing the lake after the top of the climb, there is another steep climb on sealed road but then a great descent and onto a gentle downhill gravel road.
Another section from Sachein to Brunig Pass was done on the sealed road. I think the bike route takes a gravel path which gets quite steep. The sealed road was an easy gradient to ride. The descent to Meiringen is also steep on gravel road but manageable. We rode to Vevey and then into France around the other side of the lake.
We camped and avoided restaurants owing to their expense. Camping grounds seemed similar in cost to the other neighboring countries we visited.