Well, here's my thoughts on this...not trying to dictate how it should be done, just offering another perspective. I haven't been to the exact location of this incident, so none of what I say may even be possible, but this is what I'm thinking...does anyone know if the sled is actually disabled, or if it can be driven? I'm sure this would be unknown unless someone (possibly the owner) went down to check it out, but I think it will make a significant difference in how the sled is recovered. Obviously, if it can move under it's own power (with a willing rider, or course!) pulling one of the chutes back up may be possible, even if it requires simultaneous towing from another sled or sleds up on top. Certainly easier than dragging it up.
Looking at one of the other pictures of where the sled is located (the dark 'thing' at the bottom of the chute, I'm guessing), it appears that recovering the sled up one of the next chutes uphill may be somewhat easier. It also looks like there is a low ridge that prevents the sled and avy debris from continuing down the mountain (at least in the inital direction, in-line with the chute). Hopefully this would offer a bit of a semi-flat, semi-safe zone to work on getting the sled rigged and ready to move.
If it were my sled and it could be moved/driven, but not yet recovered, I would attempt to relocate it to the area marked with the blue "X" in the picture below, as it looks like it would be less likely to be further buried or damaged by avalanche debris (including a few of the large cornices visible in one of the other pictures). Regardless of where the sled is, I'd still try to securely attach an avalanche probe (or some other long pole) to the sled so it can be more easily located after more snow has fallen. Maybe the owner has already done this, or maybe he has not been able to make it back up there, I don't know. I'd just hate to find that it's buried deeply by new avy debris, adding hours of digging to what looks like will already be a lengthy recovery effort.
As far as getting down to the sled...sure anyone could walk down there (and later, climb back up), but I do think if an experienced backcountry skiier (or splitboarder) could be convinced to take on this task, it would speed things along greatly. Skiing or riding down either chute (preferrably the "Alternate recovery chute") would likely take less than two minutes from top of chute to sled. When it's time to come up, they can put on their climbing skins and 'skin' back up as much as possible, hiking where necessary.
My other thought on this is that if there is a 'moderate' or above avalanche danger when the recovery takes place, one person gliding down on skis or a board will be able to cover the distance much faster, thus limiting their time in the 'danger zone' of the chute itself. Obviously there will still be some risk when climbing back out or towing the sled up, but I'd still aim to minimize the risk anywhere possible.
My main thought on doing all of this as quickly as possible, is to be able to utilize whatever small window of decent weather we may have to get it done. With that said, maybe the clouds will break after tomorrow's storm and we'll have nothing but bluebird for the next 3 weeks...but we just don't know, so personally, I'd plan for a short window; anything more will be a bonus!
Finally, if winching or towing the sled is the only way to bring it back up, I am thinking that the "Alternate recovery chute" may offer more in the means of anchors (trees lining the entire right side of it, as you look up) that could be used to progressively pull the sled in several stages. I'm not sure how far distance-wise the sled is from the top of the chute, but it looks to be several hundred feet. A Lewis chainsaw winch typically comes with only 150' of 3/16 cable. Even a capstan winch that could run any length of rope through it will probably need to be relocated a few times to make the pull from bottom to top, and throwing an anchor strap around a tree will be faster than digging and burying an anchor of some kind in snow alone.
Best-case scenario, if the sled starts and runs, a person could probably aim for the top of the chute and ride it as far as it goes before running out of momentum, then let it dig in and winch from there. Worst-case scenario, mark the sled with a probe and wait for some firm, spring snow, then dig it out and attempt recovery at that time. I know that if it were my sled, I would want it out of there as soon as possible, but given the weather and possible avalanche danger, waiting it out may still be the better choice.
Sorry for 'writing a book,' but hopefully something in there will be of use!