Can anyone advise how people are getting up this chute in high water conditions? I don't think it can be paddled in high water and I am not aware of a portage that can be started far enough north to pass all the high water.

look in the portage database - there is the "Staircase" portage that can take you directly from Sturgeon Narrowns to Russell lake, kindof into the NW corner of the lake

I wouldn't worry about "high water" conditions this year - its been on the low side of average, though that could change with signifiant rain. Went up it on May 31st this year and had no problems in a tandem canoe.  Getting up to the portage db mentioned isn't all that hard - start up the left side and hug the shoreline taking advantage of the eddies behind rocks and points- keep your bow straight into the current, and only as much angle as needed to move left or right - take a break here and there in the quieter water, then ferry across (if you don't know how to do an "upstream ferry" put google to work and find out) to the portage which is on the right side of the channel as you are going upstream - note! the portage isn't all that obvious as the landing is on big sloping rock (i.e. you won't see a beaten down pathway - its myabe 200 feet or so of trail)

I've gone upstream to Russell half a dozen times or more, tandem and solo - I can recall one solo trip when the water was higher than normal when it was tough going, but I made it anyway, and I think there was one tandem trip when it was high and a workout to get up to that portage, but still doable.  If you really don't want to try it, take the staircase.

Just went through there last week. It was tough paddling in against the current - we had three tandems that got through it in varying degrees of difficulty, and then I had a solo SR Tranquility, not ideally trimmed, with which I decided "no way I'm making this, gonna get out & line it".
Looking at the map, going toward Russell youd naturally think it would be best to stay on the right side. But that side has more swirlng, tricky water and if you paddled through you'd maybe want to stay toward the left initially. Pretty much what Mad_Mat said.
Going the other way, should be no problem...just have to pay attention - I'd have loved to have the camera out for all the mergansers & the bald eagle there, but it might've wound up in the water.

It's almost always paddlable- it all depends on your comfort level and skill.  Been through at all times of year and water levels, and never had a problem getting through up or down.  Okay, maybe I scraped a few rocks going down once 

Funny story about this year.  We had been paddling near a large group off and on for a day or so coming from Kawnipi.  We had both stayed on Russell.  We got on the water slighly before them and paddled past their camp, however we were kind of trolling accross Russell.  They ended up passing us seemingly in a hurry.  We caught them going out of Russell on the way to Sturgeon as they were completing the first of their carries at the portage.  You should have seen the look on their faces as we just coasted on by them.  A couple of them turned and said wtf to their leader.  My bowman waved and I nodded trying not to grin.  To be honest, I had never paddled out this way, only up it and that was like 8 years ago, so I was sure hoping I was remembering things correctly.