I'm just working in theory for now. What you could do is for your second game, code New Game to function like a special Load Game screen that only loads certain bits of data. When you load normally, we have this:
characters = Marshal.load(file)
Graphics.frame_count = Marshal.load(file)
@last_bgm = Marshal.load(file)
@last_bgs = Marshal.load(file)
$game_system = Marshal.load(file)
$game_message = Marshal.load(file)
$game_switches = Marshal.load(file) # this will keep your switches in tact, you may or may not want to do this.
$game_variables = Marshal.load(file) # same as switches
$game_self_switches = Marshal.load(file)
$game_actors = Marshal.load(file) # this will keep stats and levels in tact
$game_party = Marshal.load(file) # this will keep your inventory and gold, etc in tact
$game_troop = Marshal.load(file)
$game_map = Marshal.load(file)
$game_player = Marshal.load(file)
Again, I'm working on theory I haven't actually coded anything for you yet, I'm just getting the idea together. By keeping switches and variables in tact, you can have things from the first game affect the second one. You don't even have to use all the switches, it's possible to have the game check one or two switches (for example, a switch indicating whether or not you did an optional even in the last game) then use an event to switch every other switch off (there is also a function to reset all variables you don't want to keep).
Keeping your actors and inventory is probably most important, and be sure to keep the databases the same otherwise there will be issues.
If you have less actors and items in the second game, you'll get errors because the game will be looking for something that no longer exists. If your characters or items are different in the second game, you could get weird effects like people holding the wrong items and stuff. However, adding new characters or items to the bottom of the database should be absolutely fine, and I presume this is the main alteration you'd want to make.
So just to be clear, if you did this, you'd want to definitely keep:
Actor, Classes, Skills, Items, Weapons and Armors.
Hope this is helping, we might be able to turn it into a script soon.