Couple of questions. Why do you have to haul it for a survey. Why do you have to have a survey right now. Why not fix the engine first. Also the marina sounds like one that going to get you ten ways from sunday. I don't know if you asked or not but does the $144 cover the trip back in or is it $144 each way.
I would call around and check the other yards and prices. I'm willing to bet you can find a better deal. That $50 for paint you bring is shady in the worst way and if your paying $3 per foot per day then you should be in the work space and that should include the waste disposal. I could see requiring a deposit to make sure you don't leave waste behind but requiring a flat fee sounds funky.
Even if the engine isn't running you can tow the boat somewhere else, but unless you have a really compelling reason to haul before you fix the engine, I would pick that first.
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