I did most of that route last year with a church group.
Sag to Red Rock is easy unless it is windy. The only problems you will have is the wind and waves, some motorboat traffic until you get to Red Rock Lake and you need to stay on top of your navigation. It will take you about 3 hours or a little longer if you have wind to go up Seagull River to Red Rock Lake. Take the first campsite east of the portage on a bay. You will love it. This sunset was taken from there.
Stay one or two nights. Red Rock apparantly is not a high use lake so you might have some solitude.
Next the route through Alpine is also not bad. Pretty portage in Alpine and the lake is gorgeous. You will have no problem making your whole loop in two maybe three days if you needed to. In summer it is not a bad idea to get sites early-you can always do some exploring then. This is a picture of the falls between Alpine and Jasper.
I did not go to Seagull as we went to Jasper and then into Ogishkemuncie. You will have no real hard portages and some nice lakes and scenery. Wind can be an issue on Seagull like Sag. Let me know if you have other questions. Your most difficult day will depend on the wind. The only difficult portage is the one going into Seagull-and it is not very bad at all. You will see a lot of people in Saganaga and once you get into Alpine. Seagull is always busy. For solitude your best bet is Red Rock Lake along that route. All along the route is good fishing. Especially Sag and Alpine.