The "we need a hero" mission of The third actually kind of locks you up before you do it. I think once it is your only mission, or once you have attempted it, you will no longer be able to call on most of your homie backup until you finish both versions.
So say you go through the mission then go and save shaundi. It should give you the option to save and travel through steelport as if you hadn't finished that mission. When you do this you won't be able to call on the named homies. Everyone will be busy except for backup or the vehicle deliveries of various types.
Then if you attempt the mission again, when you get to the part where you make a choice, only the option that you have not done will be available, so you have to do the other story ending.
Once you complete the other ending, then you will be able to save again and continue traveling in steelport. Once you have finished both endings, then the homies should be available again. I haven't confirmed it, but it was listed in a couple other threads as well as on Gamefaqs. It supposedly works either way, so if you kill killbane first then your named homies will be "busy" until you save the statue.
Also, you can't do the mission a third time, so once you have done both missions your Homies will be available and you can go anywhere again.
A side note, unless it has been fixed this is another one of those "Saint's row glitches" where if you do one of the ending stories but not the other, then your homies will be locked until you complete the other ending. And it locks it for all your saves. So if you start a new game without completing the second ending, that new game will never be able to call a named homie. They will show up for the story missions that make them part of your crew, but you won't be able to use them outside of those missions. Until you complete the second ending of course.