Climb during the winter. Of course, this is significantly more challenging. Many of the first winter ascents of 8000+ meter peaks weren't until the 80s, 90s, or even 2000s for some peaks.

There are other routes on Everest, they are just considerably harder and you won't be able to be dragged up them by a guide.

Of course if you need to be dragged up by a guide you shouldn't be there to begin with.

Unlikely. As per the article due to weather conditions there may only be a few windows of opportunities to make the summit which results in the queues.