Hows this for criteria?
We draw a distinction between our elite countries (where league has a long history and is well developed) and the countries which are aspiring to development.
For Australia, New Zealand, England (or GB&I), France and PNG - our five automatic qualifiers for World Cup, you are eligible if you are born in that country, or have gained residency/citizenship status in that country, simple as that.
This allows for Kiwi kids who move aged 7-13 and grow up in league in Australia to consider themselves Australians, if they choose to recognise this through citizenship laws. No grandparent rules for these established countries, since they are considered good enough to automatically be included in the World Cup.
For any non-elite, still developing league nation (ie the rest of them), people can qualify via the above, or via ancestry basis using current grandparent rule. This hopefully encourages some decent players from elite competitions yet are below the level of national rep status to get involved in international footy, and help out the developing sides from the countries of their heritage.
There needs to be an upper limit set on how many non-native or citizened players can turn out for a developing nation (not the other way around), and this should be set at 8 (under 50% of a 17 man squad). All players' identifications of which country they may seek to represent must be recorded at the point of reigstration in an elite level competition (eg NRL, Superleague, Bartercard), and would be valid for four year cycles (matching a possible world cup representative cycle). National selectors must pledge to respect these idenmtifications, and not encourage players away during this time, but players or countries can have a window to change or appeal these identifications for whatever reasons only at the start of every four years.
The trick then is to make it attractive or equal for ambitious youngsters to represent their "rightful" country instead of (sometimes understandably) jumping ships to taste the nectar of high level rep football. This involves scheduling of regular (annual?) meaningful matches for all countries (I'm looking mainly at the Pacific here), and an examination and broadening of State of Origin.
It needs to be a three way series, to prevent players wanting to identify as Aussies (instead of kiwis, or islanders of different varieties) just so they can get into SOO. The third team could be a barbarians/others, and would include NRL based players not (eligibility-wise) from NSW or Qld, ie other states, other countries, since what makes SOO great is that is basically close to the best 34 players in NRL, bar the Kiwi/Islanders/others. One game in Brissie, one game in Sydney, one game in Melbourne each season, winner is team with most wins or bets points difference if table is tied, makes every minute of every game count, without adding an extra game to the season calendar.
Obviously need a bit of fiddling around the edges to flesh this out, mainly a reduction in club games so that in return clubs have to embrace and allow players to be involved in the developing international games. Needs broadcatsing agreement to cut 26 rounds to 22, playing each team once, and seven teams twice, and then there's four exatra weeks available somewhere... Have the international program after the grand final, just start the season a bit later (all sanctioned trials in March, proper start in April).