You should focus on the act or material that you believe your career is based on, not on which projects you thought would show your diversity, timeliness or creative potential. You really do not get that many shots in your career to get noticed. Industry folk remember the name, the material, or the circumstances and will likely have the intuitive instinct when tape number two comes in to push it aside. If it is by all means, find out what the objection was with the original submission. If you can ascertain some specific objections and if you believe that responding to these objections does not compromise your artist principles, then by all means make the necessary adjustments and respond as soon as possible.
Timing can be paramount in keeping their interest.
Out of sight out of mind has real meaning in the music business. You must be able to respond soon enough, so do not take it all so literally. What you can prepare for is not to follow in the footsteps of those who have stumbled before you. Send great material 2. Bios are for the most part superfluous, unless there is something important to say 4.