Natalya,Because you are signing the contract with a project management company and not the botanical garden, it may be especially important to include language in the contract providing for financial penalties for late payments and for neglecting to credit you for your work in the exhibit. Something like:
I think it is perfectly reasonable for you to expect to be able to use your illustrations for promotional purposes as soon as the exhibit is live. In fact, if the exhibit is slated to open, say, 9 months after you sign the contract, I would suggest you included language about being able to use your images for promotional purposes "12 months from the date of the contract or when the exhibit opens, whichever comes first." (or something along those lines -- to protect yourself in the event of significant delays).
"In the event that Client omits the credit line, Client agrees to pay an additional fifty percent of the total fee OR to remedy the omission within a reasonable timeframe."
The fact that your contract negotiations are taking a long time may mean you have more power than you otherwise might. Your clients may not want to start from scratch with another artist since there are deadlines to meet, so they might be more inclined to accept your (reasonable) demands.
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