Hi,
The HSH configuration is the most difficult if you want an all-purpose Swiss army knife guitar. For good split sounds the humbuckers need to be fairly strong so the vintage range is pretty much out.
What kind of guitar will it be - woods, construction, bridge type?
For the middle position I would look at the Irish Tour.
For bridge (I guess you meant the bridge pickup when you described "throaty"): the only BKPs I have tried in the split mode are the Miracle Man, the Abraxas and the Holydiver. All would work well.
I can mention a few neck humbuckers but I have not tried any of them split. To balance with the middle it will have to be fairly strong, e.g. like Aftermath or Painkiller neck. Miracle Man could work, too if it is a very bright guitar. Depending on the neck pickup chosen you may have to revisit the bridge position as you probably would not want a bridge pickup with less output than the neck pickup.
With so many open points at this time I guess it's best to give the BKP team a call and discuss the options.
Cheers Stephan