Hi and welcome.
The HD can certainly work, but in my mind it is a little too metal if you are going for rock and blues rock applications. Depending on how the guitar sounds acousticly (darker or brighter side, how middy, etc) there are a couple of options I would say are better for that area. My main three would be:
Blackdog as it is not completly unlike the HD, but more vintage and better suited for your application, though maybe not best if the guitar is pretty dark already.
Mule as you just canīt go wrong with that in a LP especially for rock and blues sounds, it just is the gold standard for PAF tone. Plus: What is the oposite of a one trick pony? The Mule. Fits just about every guitar ever.
Lastly the RY set can also be considered, especially if the guitar is on the darker side. It is made for LPs and delivers insanely good rock sounds, but is so versatile it can easily do tight modern metal and vintage blues also. It is a modern take on a classic sound with a nice upper mid spike and a very rocking voicing.