Am going TOTALLY by the Bible here...
Bible records what Apostles did choosing Mattias to replace Judas, did NOT say that God had approved of their selection, pretty ggod evidence that he did not, as Lord called Paul to be another Apostle!
No, you are not going by the Bible. You are fighting against it, putting forth your opinion above the Word of God. Just because you want Paul to be the 12th apostle won't make it so. Consider the facts:
1. It was necessary that someone take the place of Judas
at that time. Paul wasn't even around then. He wasn't "in the running."
2. Acts 1:14,15 indicate that there were 120 disciples praying fervently, and Mary, the mother of Jesus, was among them. The entire process was preceded by a lengthy time of prayer.
3. Acts 1:16-20: Peter arises and explains to all that there why another must be chosen to take Judas's place. One of the reasons was simply a fulfillment of prophecy. From the very fact that it was a fulfillment of prophecy is an indication that this was from the Lord.
4. Acts 1:21,22: Peter gives the qualification of an Apostle. Note that Paul does not meet these qualifications.
Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection. (Acts 1:22)
--Paul was not with our Lord from the baptism of John to the ascension. This disqualifies him from being one of the 12.
5. The appointed two.
And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias. (Acts 1:23)
--After much prayer it was the Lord that led them to do so. These men had to meet the above qualifications.
6. Now consider their prayer
And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen, (Acts 1:24)
--It was the Lord that chose Matthias; not the disciples. This, technically, was still the OT dispensation, the Church Age not beginning until the day after. Thus the practice of throwing lots. Remember also that John the Baptist was the last of the OT prophets. The entire book of Acts is a book of transition. It was God that chose Matthias through the method of throwing lots.
7. Here is God's choice:
And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles. (Acts 1:26)
--God chose Matthias in answer to the disciples prayer.
Peter made mistake by his "shrinking" back from Gentiles when Judaizers came to see him, and Paul read him "riot act"...
Peter recognized paul as having SAME apostolic authority as he did, just his was with Jews, Paul with Gentiles...
And so--a red herring. Paul lost his temper with Barnabas. The strife was so great between them that they parted ways.
Peter saw his writtings as equal to the scriptures...
--an evidence that the apostles knew which writings were inspired and which were not.
God the Fatjer and Jesus CALLED Paul as an Apostle, SAME as one of the original 12.. same role/function/position/authority etc
All of that is found in the Bible record!
And Barnabas, Sylvanus and Timothy is found in the Bible record as Apostles well. You seem to be ignoring this little fact. Why?
Paul was never considered as one of the twelve. You have provided no evidence that he usurped the choice of God in Acts chapter one.