Well first off, you don't want to use a drill, it's too brutal for a fine job like slotting a nut for a wider gauge, use a nail filer and some finer grit sandpaper. All you really need to do is evenly widen the walls, make sure not to file downward as it will cause the sting to fall on to the first fret and cause fret buzz. Second. Most string sets sold as a ready to go set, have all the wrong tensions. If you want the bass to feel smooth, the fatter the string gets and obvioiusly the lower the pitch, the higher the tension must be.
When you buy an assembled packaged string set, you get tight G, tight D, a looser A, a very loose E, and a horribly sloppy B if you go that low, and the super low F#, that's a whole other topic that needs attention, because I only know of 2 companies that makes strings in tensions for those tuning pitches. Check out Circle K strings as a starting point. The goal of a proper tension is for each string going lower to be of a slightly higher tension the the previous. So an ideal 5 string set tuned BEADG would be .39 .55 .79 .106 .150 (high to low)
So if he uses a 4 string with a drop B tuning assuming it's tuned BADG at all times take the .39 for a G, a .55 for a D, a .79 for an A, and a .150 for a B.
Now if he likes to drop it from tuning like EADG (standard) to a drop B, I say instead of a .150 go with a .128, even though it's less tension as a B, it still feels fairly good on a 4 stringer and the E would feel super tight, but very resonant. But if he only plans on using it as a BADG a .150 will sound kick ass, and will feel very uniform through out the set, so no sloppy/floppy lows. Look up Circle K strings, and check their tension/gauge chart for tensions and tunings. You can even make it a heavier set. They make strings as fat as .254" which isn't ideal to tune to B, but rather something as deep as a subcontra E (one octave lower than the standard open 4th string E), But feelwise, anything from a .150 to about their .166 should cover his taste for tension with .150 being of a medium tension and .166 being heavy.
What is generically sold as a B string in a 5 string set (.130" or .135") is a very light B and pretty useless on most basses other than maybe Musicman and some G&L basses. Trust me I've tried different sets, and if you're willing to file out a nut to a specific string gauge, go with the correct gradual tension as the laws of physics suggest. I mean have you ever seen a piano's Low B string? It looks 10 times fatter than the Bass guitar B string, and it doesn't sound bad at all, actually sounds very rich in sustain and full of bass goodness. So fatter is better when it comes to low strings. Most upright basses string sets are actually tensioned more or less correctly. They don't always follow the lower pitch/higher tension rule, but they do make balanced tensions per string, so all strings have near identical tension, which is a good alternative, but doesn't quite compare to the gradual tension theory.
There's also Gary Goodman strings. They make bass strings to order depending on your gauge and tension preference, it's like having your own custom shopped strings built to your preference. Their a bit pricier, but if you like less wrap and more core, it's the place to go to for stuff like that. Plus I think he builds on both hex and round cores and in round or flat variation. Don't remember but I believe his gauges reached beyond .288" last time I checked, there are even sound samples of what the string sounds like tuned to a recommended pitch. check them out at
octave4plus.com for more info on gauges and tension. That's about it. I know Conklin makes some random gauges past .130. D'addario has a .145 gauge with tension charts. Rotosound has a .175" string and so does Warwick. Don't know of any other manufacturers specializing in plus sized gauges. Hope this info helps. oh and by all means, do not use the .175 from rotosound or Warwick for an F#, it's good as a low A tuning but nothing lower than A flat. works great as a B string too, maybe a bit on the upper heavy side though, so a good B on a bass guitar with a 34" scale would be around .150 as a medium.