Is the feeling of guilt for not being able to supplicate for 3,000 people after offering to do so in a group, and the fear that the 'Umrah might not be accepted or that ostentation might enter the worship; justified?

Seeking prayers from a living righteous person is permissible and lawful. Benefiting your Muslim sisters with prayer is a good deed for which you will be rewarded. There is no sin upon you if you omit praying for some of them due to lack of time, and that does not diminish your Umrah. It is hoped that Allah will answer your prayer for yourself and for those for whom you prayed. You could have prayed for them with general supplications. Your Umrah is complete, Allah willing, if you performed it seeking the countenance of Allah and without ostentation.