A nice area with a number of possibilities.
First, a word of caution about leaving your vehicles unattended. Consult with Ric at CRCO to find the "safe" places. I can't remember if Lynx Lake is one of those "safe" places or not. If it isn't, it is a relatively small investment to get CRCO to shuttle your vehicles back to Missinipe and that gives you the option of choosing a route that will take you from Lynx Lake to Missinipe. You could also arrange for CRCO to shuttle your vehicles to a end point of your choosing. Ask Ric if the McKay Lake Recreation Site is still safe parking and, if so, you could consider starting just across Highway 102 to gain access to the same area.
About campsites for 4 canoes - does that mean 4 tents? There are not very many places where there are 4 tent sites. I will attempt to note larger sites, however, I'd recommend taking a good saw and some other site clearing/cleaning tools. I don't have a copy of the GoTrekkers Lynx Lake map so I'm unsure what camping sites are marked.
Possible trips:
Saskatchewan Historic Canoe Route #6 details a route from La Ronge to Missinipe via Lynx Lake, Sulphide Lake, Freda Lake and Otter Lake. Since you are planning to start at Lynx Lake it would be shorter which could allow for 2 nights at one place or shorter days. The island campsite on Sim Lake is large and campsites along the well-traveled Churchill tend to be quite big.
The Historic Canoe routes documents are available at:
https://www.churchillrivercanoe.com/tri ... oklet.html Loop Trip: Lynx, Duck, Sulphide, Mekewap, Contact, Hebdon, Freestone, Sim, Freda, Caribou, Sulphine, Duck, Lynx. I'm not sure exactly how far this is but there are a lot of portages. Most portages are relatively short but one is 1.1k and another is about 700 m. This loop could be done in either direction.
You could do: Lynx, Duck, Sulphine, Mekewap, Contact, Baldhead, Cote, Highway 102 - You could leave your vehicles at the McKay Lake Recreation Area (which has been safe in the past - check with Ric). The McKay Lake Recreation Area is a short distance across Highway 102 from Cote Lake. This would be a fairly short trip. The south pointing peninsula in Contact Lake has a fairly large campsite. The island campsite in the main part of Contact Lake is fairly large but was quite dirty the last time I was there.
If the McKay Lake Recreation Area is safe parking you could consider the Cote - Baldhead - Contact route as a starting point. You would then be able to do a loop from Contact, in either direction, as described above.
If you have CRCO do a shuttle, you could end the trip at Stanley Mission and have them pick you up there.
Another idea: Lynx, Duck, Sulphide, Caribou, Freda, Sim, Otter, Mountain, 4 portages route (Hunt, Stroud, Leckie, Lac La Ronge, then back across the northern part of Lac La Ronge to Lynx Lake. I'd have to do some research to see how far this is (my guess is that it's quite far) and involves some large lake travel.
Have fun planning!