The weight figure for the Enterprise comes right from the FJ TOS Tech Manual, they never adjusted it for the increased scale they're using in SNW.
Yeah, bummer the tonnage wasn't adjusted for the increased scale in SNW.
However, SNW didn't specify what the 190,000 Metric Tons relates to so there is some room for interpretation beyond the assumed mass of the ship...
FJ's TOS Tech Manual and blueprints state 190,000 Metric Tons as Deadweight Tonnage. Since this is the total weight they can carry then the Enterprise could be any size.
TMOST says 190,000 tons is the Enterprise's Maximum Gross Weight. This being the total weight of the ship+what it is carrying then might be more restrictive and bumping it up would've been better.
And in "Mudd's Women" Scotty describes the TOS Enterprise as "almost a million gross tons of vessel" which could be either the same as
long tons (mass) or gross tons (volume). If it was volume, "almost a million gross tons" would push the TOS Enterprise's size to a little larger than SNW's at +460m in length...which might work out more...
Six phaser banks is accurate, if you count each emitter pair as a one bank. three on top of the saucer, and three in the bottom.
I'm not so sure about the phaser bank count. I think there are also individual emitters on the top of the saucer between the pairs. In "Serene Squall" we do see a total of 6 beams firing so perhaps phaser banks do not correspond to the number of emitters but the number of generators like in TOS which had only 4 banks. Or the 6 banks means something else?