The dispute appears to be in how that grace is received. By grace through faith in Christ as enabled by Gods Holy Spirit or enabled through sacraments. Paul preached Christ as the only mediator between God and man when Jesus was already in heaven. Why would he do so if its no longer held true as you state?
Jesus Christ instituted the sacraments for the salvation of all men!
Sacramental life of the Christian church: I come that they might have life, and that they might have it more abundantly. Jn 10:10 Jn 1:16-17
Baptism: (initiation into the covenant)
Mk 16:16 Jn 3:5 acts 2:38-39 8:36
1 Corinthians 12:13 2 pet 1:11
For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit.
The Eucharist: (holy communion)
Mt 26:26-39 Jn 6:51-58 1 Cor 11:23-25
Confession of sins:
Jn 20:23 / 1 Jn 1:9 / 2 cor 5:18
Confirmation
Lk 22:32 acts 8:14-17
acts 14:22
Marriage:
Matt 19:4-6
Holy orders: (priesthood)
Jesus Christ continues HIS ministry in His new covenant church thru His priesthood in Peter, the apostles, and their successors with the same mission, power, and authority!
Mt 10:1-8 Mt 16:18 Mt 28:19 Lk 10:16 Jn 8:32 Jn 13:20 Jn 15:5 Jn 16:13
Jn 20:21-22 acts 1:17 acts 6:4 acts 8:26
2 Cor 5:18 1 Tim 4:14 Eph 2:20
Extreme unction: (anointing with oil)
1 Tim 4:14 James 5:14
The ark of salvation: one, holy, catholic, (universal) and apostolic church founded by Jesus Christ on Peter and the apostles!