Hi there!
I own a Precision Drive (first batch!), and I agree with Spikey – it's a really convenient pedal that sounds fantastic but it's not magic-in-a-box. My personal use for the PD is to use it as a seasoning on top of my patch. The patch should sound great on its own, but the PD is there to twiddle bits and pieces depending on what guitar I'm using. To achieve the same "stuff" as the PD, make good use of the noise gates, EQ, and TS effects. It's entirely possible to get those tones without the pedal, but it will take a bit of fiddling.
I'm gonna approach each point you noted here with suggestions on how to get what you're looking for, using the Tube Screamer as a starting point. I'm still pretty new to Helix, so if anyone disagrees, please speak up.
- "more tight"; okay so to me, tightness entails a low cut and possibly a mid boost, with a noise gate in play.
- "has more headroom"; here I'd suggest a clean boost in your pedal chain. Pretty straightforward. The PD propaganda did claim that a 6 on the volume knob is about 10 on most other pedals.
- "respect to definition of sound is far superior"; I'll be honest...I have no idea what you mean by this. I can possibly see this being a valid reason for digital pedals, but the PD and TS are totally analog. If I had to take a stab at it, you might mean the PD sounds brighter, while the TS feels more middy/bassy as you said? If this is the case (correct me if it's not), then tasteful EQ can transform that TS pedal into exactly what you need. I think the TS' tone control gets you 90% of the way to the right brightness, but if you need more high end, the EQ is your friend.
If Line 6 does add a PD model, I'd be super excited, but in the meantime you have the tools at your disposal to get similar tones. See how far these ideas take you, and if you find some other secret sauces to add that PD touch to a patch, I'm all ears.
Cheers, and good luck!