its a really nice thread and from the first time I saw it I imagined something like this. A new competition for one season like a cup and for example the teams that reach the top 16 will be on the next year's unified first division and etc. But that brings up also the factor of luck of the draws.
One other solution that I thought was this.(I will use the british example so its easier to understand) Lets say we start this season.
The teams that reach the semi-finals on top divisions in Wales, Ireland, England and Scotland on season 18 will be promoted to the Unified British Premier Division.So in season 19 you have 4 teams from 4 countries = 16 teams that are most commonly the best teams of those countries.
In season 19 the 4 regional leagues still exist but you have also the british league. The spots that were left on the regional leagues will be filled by active teams using the "replace bot-spot" rules.
Now during season 19 the Unified British Premier Divison will be used as the premier division and the regional leagues as second divisions , but that only in notes not in financial terms , because the actual transformation will take place at the end of the season 19 (I will explain later why I don't think doing a complete transformation at the end of the season 18 is a good idea).
At the end of Season 19, 4 teams will be normally relegated from the Premier Divison no matter what nationallity and the champs of the regional leagues will be promoted to the Premier Division. The rest teams from the regional divisions plus the 4 relegated teams will be shuffled and redrawn into the newlly created divisions in a normal way. When I say normal way I mean all the teams from the regional first divisions (now considered second divisions) will be shuffled and redrawn into the new British II.1 British II.2 , British II.3 and British II.4 (and etc to the divison III and IV).
So at the beginning of Season 20 you have the newlly created unified british league pyramid. Premier Division and the lower divisions mixed up and cleared of bots from all 4 nationallities.
The reason I say that the transformation should take one whole season to conclude is because in that way it will be more stable and more fair. At the end of season 19 the 4 most weakest teams will be relegated to the newlly created British II div , but during that season the teams in the regional divisions will not be affected in the economy factor because they will be still playing at a top country division. In that way it is giving the chance on the champs on season 19 not to be affected at all (because they will get promoted to the Premier Division). The common sense says that the more seasons the transformation takes the more stable economically it will be , but you cannot do that indefinitelly , so you need to draw a red line , and one season is a good limit. Also taking into account the bot clearance on all newlly created british divisions that solution will be even better , because there are many chances that there might be bots even on the Premier Division.
And now comes the draft issue. The solution could be really simple (and I don't know if someone mentioned it earlier). The drafts should be created regarding the percentage of teams of certain nationallity playing in that division (or in general in whole British pyramid). For example if 50% is english teams , 20% scotish 20% irish and 10% welsh , that's the percentage of the draft's nationallity in the draft pool and every teams has that chance to get a draft of each nationallity. And regarding the marketing revenue , all drafts of those 4 nationallities should be considered as playing in their homeland country (they do after all play in Britain :P ). (people even buy good drafts to train , so I don't think that a scottish will get an english great draft and will just ruin it so the English NT will not get a good player)