I own that exact guitar with the exception that mine came with a Floyd Rose and the pickups are uncovered. It was ordered new from Sweetwater around 2014. At the same time I ordered a Charvel So Cal (which cost significantly more), knowing that after A/B-ing them at home one of them would be sent back to Indiana. The Charvel was sent back . . . which says a lot about how I felt about the quality, playability, and value of the MIM Fender Blacktop.
I agree that the pickups are somewhat dark and muffled. Don't expect that removing the pickup covers will "remove the blanket." However, here's what worked for me: I approached the problem by experimenting with different magnets, finally settling on A4. Between the way in which A4 shifted the eq, along with some careful pickup height and pole screw adjustment, I was able to get a more nuanced, PAFish voice out of the stock Blacktop pickups.
With both outer coils engaged I now get a very convincing Tele tone. With both inner coils engaged the guitar conjures something approximating a “phased position” Strat. It doesn’t sound exactly like position 2 or position 4 on a single coil Strat, though it does produce that distinctive “quack,” giving the feeling of a Strat.
I also replaced those amp style knobs with regular Stratocaster knobs. The knobs on a Strat tend to interfere with my picking hand and those taller knobs exacerbated the problem.
One other nitpicking thing about my Blacktop HH Strat is that the back of the neck was super glossy and grabby. The Scotch-Brite treatment addressed that in short order.
Being completely honest here, I think I've only played my Blacktop Strat on one gig. It's not that it isn't a great guitar. On the bar gigs which have made up a substantial portion of my bookings in the last decade I've always strove to bring the minimal amount of gear to the job, the goal being able to make one trip in with everything and one trip back out at the end of the night. This means bringing only one guitar. An instrument with a Floyd Rose cannot be that guitar. It's gotta be a fixed bridge or decked Strat bridge that allows me to change a string and be back up and running in less than two minutes.
Don't worry about Furiosa's indifference. It's hard to impress a cat with a guitar. Grey cats are also very self contained. If you pluck the strings above the nut like a harp, or sound a triad of dissonant harmonics (G string 5th fret, B string 7th fret, High E string 12th fret), then their ears might perk up for a minute. But basically don't expect them to give a sh*t about your new guitar.
Happy new guitar day!