Thanks for spotting that anjouan, of course it should be "Exxon/Mobil" not "Shell" - got the companies and locations mixed up for a minute.
The point being, and hopefully it's not lost by my stating the wrong organisation, that the individual employers concerned may not be doing the negotiations themselves but may be relying on the organisation to which they are contracted.
If work stopped, the companies would feel the pressure and so would the organisation with the head contract - maybe that pressure would assist the negotiators to apply themselves.
I could be wrong, and I stand to be corrected, but from the point of view of the individual families, it might feel like their loved ones are just names to the negotiators, more so as time passes and platitudes and comments like "we're working on it" and "they'll be fine" start to seem meaningless. Perhaps something like work stopping would give the negotiators more incentive to secure the freedom of the hostages.