Moving Pokemon between all generations

[Koi Fish Lord]

Greetings, all. 

I am new here, so I apologize if this is in the wrong subforum. Now, what I am needing to do: My girlfriend and I are planning on playing all of the Pokemon games from gen 4 right up to gen 7. We both have homebrewed 3DSs with CFW and have the NDS Pokemon games as ROMS on R4i cards. The idea is to play HeartGold and SoulSilver> Platinum and Diamond> Black and White> Black 2 and White 2> X and Y> Omega Ruby and Alpha Sapphire> Sun and Moon, in that order. What we want to do is transfer Pokemon over each time we move over to the next pair of games. Each time we play a pair, we plan to catch all Pokemon available in that respective game, then move them all forwards to the next game. 

HeartGold/SoulSilver can trade to Platinum and Diamond, and Platinum and Diamond can trade to Black and White, and Black and White can trade to Black 2 and White 2, but each of these processes will take ages to accomplish, and there seems to be no way to trade Pokemon from Black 2/White 2 to X/Y when using an R4i card and a legitimate card is impossible to get in my country.

So:

Is there a way that I can batch export all Pokemon from a save (All .pkm/whatever files from the .sav) and the inject it into the next save? PkHex and PokeGen only allow for exporting and importing 1 Pokemon at a time, whereas I would like to do so as a batch to save a lot of time. I have .sav files on R4i and can make .sav backups for 3DS Pokemon games, I just need a way to transfer the Pokemon between them as a batch rather than individually.

As a nitpick: Is there also a way that I can have Pokemon moved via this method be registered in the Pokedex for the game I inject them into?

Thanks in advance and sorry for repeating myself in some parts

[Kaphotics]

5 minutes ago, Koi Fish Lord said:

PkHex and PokeGen only allow for exporting and importing 1 Pokemon at a time

Incorrect, PKHeX allows you to dump all of your boxes via Tools->Data. Can do the same for loading a folder too; dex entries are updated unless you disable Modify Pokedex in Options-> Set to SAV.

[Koi Fish Lord]

Weird, I tried it earlier and it didn't work, guess I was too quick to assume that it wouldn't work that way, just tested it and works great this time round. Also didn't know about the dex entries, mixed information online xD.

Thanks a ton