There is no benefit from having to seperate ratings, one visible for the player and one that is used ingame. That will only result in confusion by players in my opinion. I expect an increase of the number of thread about unfair match up, based on Elo, because some hidden value does the matching. As result i dont see any benefit of having a secondary hidden rating which is used in match making. Having the different ratings makes it needlessly complex in my opinion.
That doesnt mean you have some good points about how to detect smurfings and how to deal with them. I would suggest to change the current rating for that reason. So your skill is reflected in your visible Elo and used in the match making.
Things you mentioned are for example part of the Glicko-2 or TrueSkill. Both are rating systems that tries to improve the weaknesses of Elo. Both seem an improvement over the current Elo system and will be better in finding smurfs. Both should also be better in making balanced team games. Elo was meant for 1v1 games, where Glicko-2 and TrueSkill are better suited for team games.
The smurfing issue is also mainly a team game issue as result of the bad fix of the team game ratings from the devs. They are already looking into this issue.
This thread already discussed multiple solution in how to fix the current team game ladder. One of the current issues is that every account is weighted evenly, while higher rated players are probably able to carry the game for the team and have a bigger impact of the outcome. So there are also ideas to add more weight to the higher rated teams by matching teams. This makes adding smurf accounts to boost an elo of a main account much less worthwhile already. If you then also add something to the game to boost the elo of account that play much better then there rating suggest (based on long win streaks and stuff like that), then the total package seems like a good one to fix the team game ladder and limit smurfing.