how to process such photos to recover blown out grass areas while
restoring the tint to green instead of beige
Some raw developers may be better than others in restoring details/color. If you run into this situation frequently, consider testing several of the leading raw converters to see if any gives more pleasant results. My top candidates would be DxO, C1, Adobe Lightroom/ACR. Eisman and Margulis describe some advanced Photoshop techniques for this kind of restoration in their books, if you are inclined to work with channel masks, Lab and other things.
how I should take these photos to prevent blown out areas enough to
make this recovering useless
If the shadow area is small, you can equalize the contrast with flash. Larger areas can be lit with collapsible reflector like Lastolite. You can also try avoiding these shooting conditions altogether. Watch your RGB histogram. If any channel is blown out, reshoot with some negative exposure correction.
Higher bit and uncompressed raw files are usually better at this than lower bit and compressed. Make sure you are not using any crippled raw format derivative.
if I should stop bothering with blown out areas and darken them just
enough to prevent them from burning viewer retinas while keeping them
bright enough to prevent the tint shifting becoming too visible?
This reminds me of Hollywood movies. The directors of photography never make/show mistakes like that - unless it's an intention. They know what the camera sensor or the film stock can handle and accommodate the shooting conditions appropriately. They sometimes use abnormal measures not suitable for amateur still photography, but the picture quality they provide is a good inspiration.