How do you not come off as a corporate shill trying to stop people from organizing?

This is literally power being built from the ground up.

How do you get the already existing large unions to co op a movement if there is no grass roots effort?

A strike being started this way, from the ground up, will be far more effective than beginning in the unions. Unions starting a general strike gives the population a "boogey man" for why they suddenly cant go to Applebee's, and is largely a reason why a general strike has never succeeded in this country.

If a large percentage of the working force is able to mobilize and strike, protest, sit in, all across the country without needing a central figure to claim ownership there is no one for the right wing talking heads to point fingers at and scare our grandparents into voting for union busting politicians.

Stop trying to discourage people. May is awfully close and getting anything on a large scale going might be a daunting task, but it isn't impossible. If it fizzles out, which is highly likely by the way in my opinion, at least we are able to educate people on what it takes and make it clear to those we reach that doing something like this is actually possible and not outside of the realm of possibility like you so desperately want to make it seem as.