The stealing of a pokemon is rarely a MAJOR plot point(Peeko the Wingul from RSE and the Purrloin from B/w2 are the olny example I can think of at the moment) and it has neve been the PLAYER's pokemon so...
The thing is getting to Hoenn and not having you pokemon needs to have a short and simple reason for it and you need to also have a short and simple reason to get them back afterwards
obviously the PC has the simple connectivity thing so that is mostly a non issue
the real issue is your party
having Team "X" take your pokemon would create a complex story in need of alot of plot support
they cant simply take your pokemon
you have to take them back
and since you have to not be able to use them til later that means they have to show up later(after the E4) when the "bad guys" have already been beaten which means there has to be a different reason why you cant get them back imediately after beating Magma/Aqua(which shows why it cant be them) after the end of our modified TR story(you will see

) they are completely scattered and will not be coming back any time soon so it cant be them thus we need a new bad team which means they need backstory and motive(even just being a bunch of people out to steal and make money needs to have atleast that much explained) and also new NPCs and such
With the prof we can have them explain that since you wont have access to the PC(connectivity issues can be a well known issue) that maybe catching new pokemon a raise them would be a better idea for you and that they can care for your original party as well as study the effects of being raised by a "good/strong" trainer has on their growth and development.
TL;DR: Enemy teams need alot of plot and development to explain something that can other wise have a simple and easy explination...