1. James had just told us to go to the presbyter in verse 14 for healing and the forgiveness of sins. Then, verse 16 begins with the word thereforea conjunction connecting verse 16 back to verses 14 and 15. The context seems to point to the "elder" as the one to whom we confess our sins.
2. Ephesians 5:21 employed this same phrase, "to one another," in the context of teaching about the sacrament of holy matrimony: "Be subject to one another out of reverence for Christ." Even though the text says "to one another," the context limits the scope of the meaning of "to one another" specifically to a man and wifenot just anyone. Similarly, the context of James 5 bears out that the confession "to one another" refers to the relationship between "anyone" and specifically an "elder" or "priest" (Gk. presbuteros).
3. The final words of the passage speak specifically of ministers called by God to minister to his people in his place, i.e., Elijah the prophet (cf. Jas 5:17).
I know what you would like it to mean, but it does not.
The context is that sin can make you sick. Believers should confess those sins to the one they wronged. They should also pray for one another with that person.
Your comparison to Eph 5:21, refers to husband and wife (one to another) - not the elder who was marrying the couple. As such it is a good comparison. The elder would do the act of marrying the couple. The couple would do the submitting one to another.
In verse 16, the elders (not priests), are anointing and praying for the sick person. The sick person, if her sickness is due to a sin against another, should confess to that other. Much affliction stems from those kinds of sin and should be resolved.
Only eisogesis takes a later idea and tries to squeeze it into passages that refer to something else.