From my point of view, Jelastic is what you definitely need, because it meets the stated requirements.
First of all, you can stop your environment at any time and will not use dynamic resources (RAM, CPU). Therefore, you will pay for the actual resources used.
Alternatively, you can manage this request directly with your hosting provider.
Jelastic plans to open an API that will allow users to control the cycle of their environments (stop, start), which can be placed on your code or implemented in a browser. This will be done in the near future, so do not lose the opportunity to try.
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