LOL.....if you want a complete solution, I am not paid enough to come up with that. What I have offered are ideas towards a solution. Let the experts figure out the exact details.
However, before talking about a solution, people first have to decide whether there is a problem and thus a need for a solution. I get the impression that you don't think the current system needs fixing?
If you did want to discuss need, the first notion we should explore and what seems to be a sticking point for many is the term "judgement call". IMO, most of the decisions a referee makes are judgement calls and made "in his judgement of what he observes at the time". Whether its crossing the goal line, stepping out of bounds, completing a catch, interfering with a receiver, down by contact, grabbing a face mask, horse collar tackle, hitting a QB late and on and on. Basically, he is on the field trying to enforce all of the rules of the game. What was decided a long time ago was that refs weren't always seeing things clearly and that their judgement of what happens on some plays was proven time and time again not to always be correct and those errors were seen as critical enough that they should be subjected to being reviewed. So replay was instituted to try and correct certain calls when the refs judgement was in question.
So now people will say "well jeesh, the ball crossing the goal line, a receiver having 2 feet in bounds, completed catch, those aren't strictly judgement calls, they are calls that can be made more clear and concise with replay and should be enforced/ruled upon as per the rules of the game. Yet at the moment those plays are initially ruled on by a ref, they were so with split second judgement calls, calls made based on what the referee saw or didn't see at the moment they occurred, right or wrong, they relied on the Referees best judgement of what happened and then open to be reviewed in case that judgment was off.
Now we have progressed to the sacred cow or the current dividing line of "we can't use replay to question a ref calling or not calling a penalty no matter how it impacts the play/game". Yet, having 12 men on the field is a 5 yard penalty and can be challenged. What makes that a special penalty, refs aren't expected to be able to count up to 12? The league reviews hits after the game and fines players, even if a penalty wasn't called at the time, so that kind of a review is ok? Are all penalties just strictly judgement calls and a referee should never be questioned that he missed something, didn't follow the rules correctly, his judgement for whatever reason was off on that one play? No matter how it impacts the outcome of a play, that is ok, because it is an acceptable error in judgement and thus part of the game? He throws the flag or he doesn't, case dismissed?
Replays during and after games have proven time and again that referees aren't perfect and have missed all sorts of calls for various reasons. Thankfully, some of those can currently be corrected via replay, but missed calls on almost every type of penalty is some how immune from that process, why?