My primary problem with the casual use of the word "Persons" is that it gives the distinct impression of three independent beings standing around having a conversation. The concept of the Son and Spirit being subsumed in the Father is lost, and tri-theism all-too-quickly rears its ugly head.
I really don't think we have a substantial disagreement here--just different preferences in the way we're phrasing it.
Shalom.
24then -- the end, when he may deliver up the reign to God, even the Father, when he may have made useless all rule, and all authority and power -- 25for it behoveth him to reign till he may have put all the enemies under his feet -- 26the last enemy is done away -- death; 27for all things He did put under his feet, and, when one may say that all things have been subjected, [it is] evident that He is excepted who did subject the all things to him, 28and when the all things may be subjected to him, then the Son also himself shall be subject to Him, who did subject to him the all things, that God may be the all in all.
My understanding is that Christ subjects Himself to God, and that the person of the Father is a primacy in understanding the tri-unity.