Not really. You could put it back the way it was, then put resistors in series with the neck and bridge pickups to limit their output when selected singly. Then, all positions would be at roughly the same level. But, it would be a lower level overall, which probably isn't desirable. You'd have to amplify it more, which even when using noiseless pickups is going to narrow your S/N ratio.
The problem is that you're using three humbuckers, whereas on a standard Strat you have three single coils, with the middle pickup being reverse-wound and reverse polarity. That has different effects when you're noise cancelling or running in parallel. With the humbuckers, putting one out of phase with another while in parallel causes their outputs to cancel each other. The only reason you got any output at all that way is the pickups are slightly different and are in different physical locations, so the signals weren't identical and couldn't cancel each other out completely. But, what was left wasn't very useful.
With single coils, the middle pickup is reverse-wound/reverse polarity, so putting it in parallel with the neck or bridge pickup is a natural phase inversion that tends to cancel common signals rather than differentials. So, you get a bit of noise cancellation and a sort of comb filter effect on the signal. That's where that "quack" comes from. It almost acts like a bandpass or notch filter, depending on how you look at it.
I think that may be part of the argument that says "noiseless single coils" (which are actually just reconfigured humbuckers) don't really sound like single coils. Well, the latest and greatest ones sound remarkably close, but they won't behave the same way single coils do in a standard Strat setup when you try to do what you're doing. But, that's not necessarily a Bad Thing. It's just different.
One thing that might be worth investigating is
the Bill Lawrence "Q Filter". It's an LCR network built into a little 1" sq. block that you put in place of the capacitor on your guitar's tone control.
I've not used one so I can't say exactly how it behaves, but those who have are usually pleased. They're a little more expensive than your typical tone cap at $24, but in the grand scheme of things, I don't suppose that's a great deal of money.