I work at a non profit and we just won union recognition and are slowly moving towards first contract negotiations and I HAVE NO IDEA WHAT I'M DOING. Would love to chat with some folks about their experiences, especially if you've negotiated around contracts/grants/etc.
This is a weak point in your setup then, it is the same exploitation of nurses and other care workers. The culprit is the boss and company that doesn't agree to the conditions or broke agreements. They are responsible for a strike.
Would your boss work without pay? That is what people demand when they are angry at people striking. The effects of collective bargaining are to the benefit of the group you are working with.
I don't have any relevant experience so just thinking out loud here. Is some way to platform the voices of "clients" with pro-union sentiment to really drive though the point that the strike is ultimately for the benefit of the clients as much as for the workers and build solidarity on that axis?
Yes, creating a base of support in clients can be good. However companies in bad jurisdictions () sometimes retaliate against individuals for "breach of confidentiality". However if you are protected or are secure it can be an asset.
In the case of the Charité Bettenstreik (hospital bed strike) the nurses, doctors, hygienic personal etc. were attacked for abusing the poor sick people. Yet the strike contained quite important points for their Quality of Care and Quality of Life as well as that of the workers. The workers wanted to have at least a second person at night at each ward.
There are literally PhD thesis and research thesis about that and similar hospital strikes. The point is that people in care for and you are somewhat part of it are abused due to the good they do (christian "unions" are even saying why do you want money or good conditions if you do moral stuff and are getting a benefit after death?). The right media and often bosses will side against you if there are hot industrial action or collective bargaining situations. To have prepared some support with the stake holders and "customers" of your work is good, especially for people who don't want to hurt them, but after all if you win it will be better for the people you work with.
Talking to people about stuff that bosses will do during collective bargaining is called inoculation it is quite good and it helps to do organizing inside your work place on one hand and get experienced organizers/activists who also tell your activist allies how bosses will retaliate.
So your point is a very well made and very relevant one.
As others wrote structure tests are extremely important, see who is active and who is active when and willing to get involved. To know your true power (even if it is just distributing flyers, etc.) is quite important.