The scooped response is from the filtering. You can get that either with filtering a feedback loop or filtering another part of the circuit.
If your goal is about HiFi (and HiFi helps set you up for a nice scoop* by flattening the response and increasing the audible bandwidth**), then by all means include global NFB.
*but the scoop comes from filtering, not from merely adding NFB. So you still need the filtering.
**from the audible perception of balancing the frequencies (whilst reducing the amplitude all round)
I wouldn’t be too concerned about reducing gain from having an unbypassed cathode resistor on one of the EF86s - bypassing the screen has more influence on gain in a pentode (than bypassing the cathode).
If you aren’t concerned about HiFi and just want a mid scoop, you can play around with filtering the cathode resistor bypass network (and/or the screen resistor bypass network).
Another way of getting a ‘cleaner’ signal (albeit with reduced gain) in a pentode, is not having a screen bypass capacitor. The screen will still act to boost the gain (above what it would be in triode mode), but the screen current feedback within the pentode will keep a lid on the gain. You will lose some (but not all) of the ‘bite’ of a pentode, but the added compression from an unbypassed screen can also be pleasant in a guitar amp (if you have enough gain elsewhere in the circuit).