The Picard Maneuver thing could always be explained to be a special tactic only applicable in situations where the opponent's FTL sensors have been damaged.
Since our heroes in all the Trek eras emphasize that "natural phenomena" do not travel at warp speed (apparently, lifeforms don't count), any FTL sensing would be unnatural and "active" and could be observed. It is customary in Trek for individual systems such as transporters or weapons or communications to unpredictably go down in battle while the rest of the ship continues to work. So, there would be every dramatic and logical precedent to Picard realizing that the Ferengi had just lost their FTL sensors and could be surprised by a warp maneuver, provided he made a surprising
maneuver and didn't needlessly alert the Ferengi first that their sensors weren't telling them the whole truth.
Outside this special case of Battle of Maxia, the Ferengi probably are adept at sensing at high FTL speeds. After all, their ships are among the fastest in the neighborhood, and would require navigation aids to match.
Picard's faked log spoke of mistaking a sensor cluster for a weapons bank. Perhaps that's actually what happened? Perhaps the real Picard, once forced to fight, knocked out the Ferengi FTL sensors when attempting to humanely silence their weapons?
Romulan and Klingon space, which happens to be on the other side of the Federation from Cardassia
Does it? Klingons once had a border quarrel with Cardassia, at the Betreka Nebula ("Way of the Warrior").
And while there are no direct references to Romulans sharing a border with Cardassia (just to Romulans operating at the "Cardassian border", which might be their border against neutral space, in "Improbable Cause"), there are indications of ongoing Cardassian/Romulan intrigue (say, Terok Nor featuring Romulan components in "Dax" - technological aid or espionage?). And "Birthright" has Worf take a ride in a small and thus supposedly slowish craft from DS9 all the way to Romulan borderlands, suggesting spatial proximity. So the three villain realms might actually be within easy travel of each other, with only sparsely populated parts of the UFP in between at most, and we'd be none the wiser about the ability of the UFP sensor systems to monitor intrusions into "UFP proper".