Which brings me to the next question. What are the advantages to increasing neck relief over raining string action or vice versa?
Either way is a legitimate approach. However, if I was operating on my own guitars, I would simply raise the action because it is the easiest to do and also the easiest to undo. I also don't like to ask the wood in the neck to possibly assume more than one position. Once the relief is properly set, raising the action will cause no significant change in string tension.
Having said that, allowing more relief in the neck will cause the string to fretboard distance to increase more quickly than raising the action. It will also (IMHO) make the instrument much less playable as you move up the neck. Either solution will make it less comfortable to fret, but allowing more relief will raise your string action at a much lower point on the neck.
Allowing more relief will have a more dramatic effect on your intonation, since for a larger part of the neck, you will have to push the string down farther to contact the fret, with the higher fretted notes going sharp much earlier than by simply raising action.
Again, either option is a trade-off for the sake of using a slide. One way to lessen the downside of either method is to increase your string thickness. If you're used to using .010s, you might bump to .011s or even .012s to allow better slide response. Obviously the downside of this is going to be your fingers when you fret notes. More effort will be required. It may also be necessary for you to reset your neck relief and possibly increase the nut slots to allow for heavier strings. None of the alternatives is a panacea and it is really up to you which way you go. It's your guitar and only you will know which option will work best for you.
My slide playing sounds like I'm murdering cats, so the three slides I have around the house rarely get used.