Having worked for the chamber and organized dozens of evacuations - the park does help, and in fact is the primary point of contact for most emergencies. They have two speedboats operating inside the park - when the park is open and operating. In addition, they need to be involved in any evacuation that involves helicopters (rare, but it happens). These services are not available before the park officially opens.
I am sorry to say Steven - but when coordinating these evacuations I have personally sat on these speedboats supplied by the National park on at least 5 times. The boats are smaller, faster and designated for these purposes. They do not operate at night for safety reasons, and if an emergency happens at night, we would use the services of private operators. These policies may not still be in place, but this was the procedure the four years I coordinated evacuations.
Something very important to consider:
It is illegal to enter the park during these closure times - as noted above. As the parks are closed and it any activity inside the park is illegal - insurance companies do not cover such activities (read your policy). Yes - many insurance companies do not do thorough investigations and will pay out in case of accidents. However, there has been cases of insurance companies not paying claims.
Any operator, agents and potential client who respects the laws of Thailand (and elsewhere) needs to be applauded.