I don't think your proposed format, with the league stage at the end, will get the teams back into the national cup at a suitable round. You proposed 3 knockout rounds and 5 league rounds. In a country with 4096 teams, 8 rounds would reduce the field to 16 teams. But if you have the 6 finalists entering the national cup that means you have to only have 10 teams advancing from the national cup, so you reduce your starting field for the national cup to 2560, simply so you can have a league stage.
So I think you should stick with a straight knockout. But 64 works better than 48, so go ahead and take 2 teams from each III league.
National Cup: 5392 teams.
Divisional Cup: 64 teams
Preliminary Round (NC only): 3488 teams play, 1904 byes.
Round 1: 3648 in NC, 64 in DC
Round 2: 1824+32 DC losers in NC, 32 in DC
Round 3: 928 + 16 DCL, 16 in DC sweet sixteen.
Round 4: 472 + 8 DCL, 8 in DC elite eight.
Round 5: 240 + 4 DCL, 4 in DC final four.
Round 6: 122 + 2 DCL, 2 in DC final.
Round 7: 62 + 2 DC finalists.
Round 8-12: 32 -> NC champion.
That will work OK for countries with 5 or 6 divisions.
Does the DC champion win a spot in the BBB?