I have stumbled upon a few tunings that I like, and also found what I believe to be the closest thing to an answer that I will get.
The people in these two links give different tunings, plus possible solutions to problems that occur.
I think the best and closest way to do it (for most songs) is to take off the E and G string, leaving the A and D. Tune the A string up to D, and tune the D string up to A. This makes the strings more tense, which makes playing in the first few frets a lot more comfortable. The person in the first link says the same thing, although I discovered this myself.
The problem is, Sandman used multiple tunings in his recordings. For instance, in some songs both strings were tuned the same note. To try this out, I used the A and G strings, tuning the A down to G. Although G is probably not the tuning he used, you can still play a few songs correctly. Also, I had suspected for a while that "Buena" was tuned to C. The person in the first link above seems to agree with me. I will try all of the tunings he mentioned, and any more that I stumble upon.
While I was playing today, I noticed that even though I had raised the action considerably on the bridge, the strings were still pretty close to the fretboard near the headstock, which made playing the lower notes uncomfortable. I think adjusting the truss rod could have some effect, but I am pretty sure the only truly effective solution would be to somehow raise the nut. Again, the person in the above link thinks the same way.
It's funny. I have encountered the same problems that the people in those links have, and thought of the same conclusions. I have discovered some of the same tunings that they have. It must mean something.
I really must commend Mark Sandman. He must have done LOTS of work to get his bass to cooperate with him. He must have encountered the same problems I am going through, and he definitely overcame them. I know that he probably spent many hours tweaking the sound of his bass before he got it just right, and it payed off well. Even when I fix all of the problems and find the best tuning, I am still going to have to learn to get comfortable playing with the slide. I can definitely play it, but it doesn't sound anywhere near as clean as Sandman played it.
I know that all this work is going to pay off quite well. Heh, I have even incorporated the slide into my regular bass playing. Later today I am going to go to the guitar store to buy a better slide, some pics, and flatwound strings, then take a few pictures of my bass. More to come.