Good luck but, a picket, strike, or anything resembling a "strong-arm" showing does not have the same effect in this industry that it would in the airline industry. People are not loyal to airlines, they go for the cheapest ticket. In our industry, as we all know, the customer is a different animal and not part of the sheep in the rest of the world. The way your customers will view this is paramount to the effect your picket will have on a select few at your home office.
There are two ways it can be viewed by your customers; the company treats its employees negatively or the employees are dissatisfied with their company. Both of which are, well, bad. Do the customers know how business works, yes. Do they understand these kind of things, yes. At the end of the day though, there are going to be those customers that will think that their service is being compromised in some way by the negative impact of this display. You're not happy, otherwise, why picket? That is how it is viewed, like it or not.
I understand what you're doing and hope it works out but, I don't think anyone realizes the impact this could have on your customers. What if there are potential customers or existing customers visiting the home office the day of the picket?
I understand the need for this and you guys are in a union but, I have to think as someone said earlier that 6 figure employees picketing just doesn't look right in this industry (my opinion); however, we'll take any disgruntled customers that want to leave. Good luck.