I am a mountain and sea kayak guide. I have led a number of trips in the Sierras and have done numerous solo hikes on and off trail in the Sierras including the whole JMT.
The following IS NOT a comment on any fine folks who have written here. However, well intended, skilled, etc. there are good reasons to not go with strangers on such an endeavor, imo.
I would recommend that you look again at the idea of hiking with strangers in any area, including the Sierras. This is not an I am a guy you woman sexist comment, same applies to guys imo.
It is from many years of experience with people in the wilderness. ANY TIME you go that far from definitive medical care, and stress your body and take on a degree of risks people's judgment, personalities, and decision making become suspect at times.
It is a large error to think that there is automatically safety in numbers. Actually it depends on the level of skills, critical decision making, fitness and cohesiveness of goals, expectations, etc.
The actual risks may increase due to peer pressure, bad decisions, and wrong actions should you become ill or injured.
I ALWAYS approach such trips as if I am solo and think out how I would be safe, happy, and able to take care of any situation. Then I can realistically leave a group if necessary and my own decisions are made clearer to me.
Finally, I think the idea of going on an extended trip with strangers is highly likely to be less than good. Would any of us go on a blind date for a week? There are numerous reasons we have better common sense but not on hikes for some reason.
Yes, by all means go ahead, but do consider the thoughts above gleaned from many experiences out there. IMO, at least go on an over night hike with proposed folks or even better friends who you know and have camped with before.