I second @Mike's point, "There is a difference between accepting a job offer and starting a job."
Of course accepting a job and then rejecting it is not ideal, but you are not in a unique situation and it probably happens often enough to be understood and handled in the HR world. The larger the company, the higher the incidence of such events, and the less of a big deal it is.
Until you actually begin working, you don't owe anything to your prospective employer, and are entitled to change your mind. Life happens and businesses recognize this and treat it as a matter of fact, not take it personally. If someone does, it is their issue.
Think about it this way: what is worse for a business, someone accepting and then rejecting an offer prior to starting, or starting a job only to leave a couple months later after some overhead costs of time and resources have been invested in their on-ramping? From this standpoint, you are being proactive and acting in the company's best interest by changing your decision earlier than later.
As has been mentioned, this depends a little on how tight the industry is and whether "everyone knows everyone" or there is some flexibility and anonymity in this professional space, where a decision like this would be "contained" and you will be able to move on with your career growth without adverse impact. This is less of a concern if you are geographically mobile and/or are relocating for either of your jobs.
With this in mind, my suggestion would be to act in your own interest and hedge your bet by accepting one of the jobs with the shorter notice, but postponing the start date a little (maybe by 2 weeks) to buy time and find out the 3rd company's decision. If they don't offer you a position, nothing is lost; if they do, even better. Win-win.
One final consideration. If you accept and then reject an offer, the company HR dept might make a note of this in their system (assuming they have a system for tracking recruitment process and status for each candidate). If they retain this kind of historical data, this might be a slight disadvantage if in the future you decide to reapply for a similar position with this company, especially in the same department/organization. Here it is helpful to have a broader career outlook and realize that the world does not begin and end with a single company, in fact there is an enormous variety of firms and jobs and your options are only limited by the constraints you place on yourself (geographic, continuing education, etc.).
In the broad scope of things, this is probably not a major hurdle, or any hurdle at all. Even if you decide to come back to them later, having some kind of 'history' in their system does not necessarily mean that that door will be closed for you; it is also entirely possible that the management will be changed by then, and your past effort applying to this firm may be reframed as evidence of your interest in them. There are multiple ways to frame any issue.
Again, to restate the point: even though accepting and rejecting an offer might seem awkward to you, managers don't have time to dwell on such issues. Good luck!