What strategies do you employ to maintain a balance between creative effects and the technical limitations of the project's budget or timeline?

Since there are several approaches to the same visual effects result, one way to adapt to a tighter budget or a tight timeline would be to use pre-rendered assets from a marketplace such as Motion Array, Storyblocks or Envato. You can usually find high quality assets that are easy to add into your composition, but of course lack customization or might not have the camera perspective you need. 

Another strategy that is getting better every day is the use of AI in VFX generation. The current technology is getting better every day and is limited on the output resolution, but in a matter of months it should be on par to standard project requirements in FullHD or 4K. AI generation handles pretty well complex vfx such as explosions or generation of landscapes, even fantasy backgrounds you can later use to replace a green screen. This could be a way to provide high quality effects at a fraction of the price, while also saving time.