Best Offset for Garage Rock?

I have a Stratocaster and it's a great all-rounder, minus the quacky sound that I hate. I want something that I can get a cruncher and fuzzier tone out of and I'm happy to mod it to oblivion in order to get there.

Tonally, I want a 2000s rock-blues/garage rock/Indie sound like White Stripes, Black Keys, QOTSA St Vincent and others. I also like indie, but a lot of that is covered by the strat.

I recognise that amp and pedals play a large role, but am handling this and would specifically like recommendations and thoughts on what guitar to buy.

I'm looking at Mustangs as part of the Classic Vibe, Fender Vintera, Player Models and the Fender p90 models.

I think that the CV would be a great option for modding as I'd save money upfront and spend the savings on mods. The CV line also features the floating trem and the pickup switches. Whilst these aren't essential, I do think that they're nice to have, though, if they are not great out of the box then they're not necessarily an advantage as I would upgrade them.

Previously I considered buying and modding a tele, but dislike the country twang. I also considered a jazzmaster too but find them a bit underwhelming. I think I'd like a Mustang after watching videos and reading about them. They seem to generate a satisfying fuzzy sound, whilst also being capable of generating nice indie tones.