it is not a problem to be solved if op just wants to maintain the exposure ove avery long period of time, costs are de minus mus. if op wants to start an passive etf fund and make money by collecting management fees, that is a different ball game.
No, implied financing cost spreads of futures a.k.a. replication cost are not de minimis, but substantial and recurring, as are annualized swap spreads. Like I predicted, this is not a subject that traders are typically interest in.