Done a few different variants of this recently.
Starting at Braithwaite and going over Coledale Hause and Whiteless Pike is best.
Don’t be tempted to take Gasgale Gill instead of Whiteless as it’s taken a lot of damage in the last big storms and much has been washed away. Gasgale no longer flows and you’re forced to take unridable lose shale climbs to detour around.
Up the front of Red Pike (Sourmilk Gill) is a brutal carry.
The traverse of the High Stile/High Crag ridge is mostly ridable but very stop/start obstacle-hopping in places and not that interesting apart from the views. There’s one super-steep stepped descent towards the end of the ridge that is technically challenging but ultimately not worth the long climb up Red Pike to get to it IMHO.
The descent back down Scarth Gap to Buttermere, which you’d have come up when doing 4 passes route, is ridable but not really as much fun as you’d expect in the top half. Tough going but a bit underwhelming.
If doing Red Pike, I prefer to go up via Scale Force/Scale Beck and come back down Sourmilk Gill. Scale Force is still a carry but saves you doing Red Pike as an out-&-back. I’ve done that route twice in the last year, once on a full sus in the dry and once on a hardtail in the wet.
Dry & full sus = great brutal tech descent.
Wet & hardtail = almost unridable in places, felt like I’d taken a knife to a gunfight.
Recommended return leg from Buttermere to Braithwaite = up Sale Beck and down Rigg Beck. Optional detour over Causey Pike instead of descending Rigg Beck.
Even without Causey Pike, it’s a big day out. 6000 feet in 20 miles.