As a baptized Christian, you’re not the person that the RCIA is meant for, really. You are already a Christian, but not in communion with the Catholic Church. What’s necessary is for you to make a statement (i.e. profession) of faith that you believe everything the Church teaches as being divine truth revealed by God, Who can neither deceive nor be deceived. Such a reception into the Church need not happen at the Easter Vigil, and the US Bishops actually advise against it, as you have pointed out yourself:
For those who have been instructed in the Christian faith and have lived as Christians the situation is different. The U.S. Conference of Bishops states: “Those baptized persons who have lived as Christians and need only instruction in the Catholic tradition and a degree of probation within the Catholic community should not be asked to undergo a full program parallel to the catechumenate” (NSC 31). For this reason they should not share in the same, full RCIA programs that catechumens do.
The timing of their reception into the Church is also different. The U.S. Conference of Bishops states: "It is preferable that reception into full communion not take place at the Easter Vigil lest there be any confusion of such baptized Christians with the candidates for baptism, possible misunderstanding of or even reflection upon the sacrament of baptism celebrated in another Church or ecclesial community . . . " (NSC 33).
Rather than being received on Easter Vigil, "[t]he reception of candidates into the communion of the Catholic Church should ordinarily take place at the Sunday Eucharist of the parish community, in such a way that it is understood that they are indeed Christian believers who have already shared in the sacramental life of the Church [that is, Baptism] and are now welcomed into the Catholic Eucharistic community . . . " (NSC 32).
But in order to be able to make such a statement in good faith (no pun intended), you would probably be expected to undergo a period of instruction/preparation, perhaps with a priest, catechist, or sponsor (for Confirmation). It sounds like you’ve done some studying on your own – good for you! – so you should meet with a priest at the parish at which you would like to be received.
You will also be in need of the Sacrament of Reconciliation before you would receive your first Holy Communion.