The bottom line as that we really don't know... sometimes just plain old tincture of time is enough. But here are my thoughts, if you take them with the understanding that this is just based on what I think, not on much evidence.
Caffeine increases CSF production so helps to reduce symptoms from low CSF volume and pressure. Just try it and see if it helps at all. I need pretty large doses to make a difference, but animal data suggest that chronic daily ingestion is superior at upregulaing CSF production rates. I was not a coffee drinker before the leaking started!
If we assume that the cervical dural puncture left you with a post puncture leak, then bedrest will help your symptoms because the CSF you do have left is not all pooled in the lower spine. The pressure in the head and lower back become equal when horizontal, instead of very low in the head and higher at lumbar level when upright. Simple hydrostatic pressure...
For healing, it is thought that keeping the pressure at leak level (if known) lower rather than higher, to reduce the rate of flow of CSF across the leak, might be better. For a cervical leak, by virtue of location, being completely flat might not be necessary to minimize pressure gradient at that level; head a bit higher than butt might be better. The problem is that your head might not tolerate being inclined much.
Avoiding lifting, valsalva and binders might be preferable to keep the pressure gradient lower. If you want your head to feel better temporarily, then wear a binder (but expect increase flow thru leak). I would not tie a scarf around your neck.
If I were in your shoes, I would avoid things that increase intracranial pressure, like bending, lifting and valsalva, but avoid getting deconditioned by doing some walking and maybe recumbent biking. Spend a fair bit of time semi-reclined if your head can tolerate it. If your head is not too bad fully upright, then that's likely okay with a high cervical leak. Don't do a lot of neck rotation at extremes of range.
It never hurts to pay attention to good nutrition but isn't likely to have a big impact for you in the short term.
Did your neurologist ask you to wait another full month then try another EBP? Or what? Is that negotiable?
Can you share the details of your current symptoms?