late registration can be done pretty simply just by adding players to the tournament, players who have busted cannot re-enter a freezeout tournament - that's why it is called a freezeout, the only real exception to this is freezeout tournaments where a special house rule allows a player in the first 6 hands or in the first level etc to buy back in, but again that is still a re-buy, even though it is not a re-buy tournament.
If you want to allow busted players to re-enter a tournament it would have to be a re-buy or add-on tournament. I don't see why you can't have re-buys during your late registration period, that's what they are for!!??
EDIT - you still don't need to call it a re-buy tournament,although technically it is if you are allowing players to buy back in.
Add-on's would mean that players not out would be able to buy additional chips. In any tournament or software there is no way to allow re-entry to a tournament, unless you are offering re-buys or an add-on can be used as a re-buy.
Stuart