I'm surprised you find it bassy as when I tried the Tremonti, I found it to be about the same as my Custom 24, which is warm but quite balanced overall; perhaps a little down on the treble. The Abraxas could be a good choice as it's very versatile but compared to a Nailbomb it will be nothing like as tight with a much softer bass response. The Rebel Yell would be the next step down from the Nailbomb and is apparently a versatile pickup but has more upper mids and can therefore come across as rather aggressive. Thinking of your church playing, this may be a bit too much and the softer and smoother response of the Abraxas would sit better in that environment. In fact, I think a better compromise might be the Holydiver. It's tighter and more aggressive than the Abraxas but nothing like as extreme as the Nailbomb and Rebel Yell. It has the smoothness and the extra mids of the Abraxas but enough tightness and aggression to become an extremely versatile pickup. For me, the Holydiver gives you a better balance between the two styles you're after, though I'm sure you'd also like the Abraxas. If I had to pick a third option for you, I'd be inclined to suggest the Black Dog.
