As for the screencaps, I view it as more of a "forced perspective." That is, the Stargazer is actually much closer to the camera than the Enterprise is, and the tractor beam is coming from the Enterprise from an angle instead of being on the same plane as the smaller ship.
This would make some plot sense in that the ship originally might fly between the E-D and the Ferengi vessel, as part of the hand-over ceremonies or whatnot. Since the later footage is achieved simply by removing the Ferengi ship, the angle of the tractor beam might be taken to remain constant.
FWIW, the comparison in "Peak Performance" suggests a smaller Constellation
, basically conforming to the proper scaling of those LN-64 -style nacelles.
Incidentally, it's fun but sort of unexpected that this ship type indeed seems to have "main" and "non-main" phasers, as the dialogue of "The Battle" would suggest. In addition to the regular twin emitters on the saucer, there are these single emitters closer to the rim!
And even though these only seem to be part of the real topside, not of the inverted top that forms the saucer bottom, we could speculate that the bottom, never really seen up close on screen, does have them as well - this would be the weapon seen firing in the above wargames shot!