There are two senses of the phrase "Apostolic Times." The first, central meaning would be 33AD-100AD, the time period between Pentecost and the death of the last Apostle (John, in either Patmos or Anatolia.) There's a larger sense which would include the Apostolic Fathers, that is, the first-generation disciples of the Apostles, those who learned from the Apostles personally. That would extend the time-frame by a generation: AD 33 - AD 160 or so.
This list shows the span:
•Clement of Rome (ca. AD 15 - AD 99) was consecrated by St. Peter
• the author(s) of the Didache (written sometime between AD 50 and AD 110)
•Ignatius of Antioch (ca. AD 35 - AD 110) early bishop of Antioch, was taught by St. John)
•Polycarp of Smyrna(ca. 69-155) also a disciple of John
• the author of The Shepherd of Hermas (written between 140 -155)
The problem with including these as "tradition" is that the teachings in some of these contradict what the apostles and Luke wrote.
For example, in the Didache, which was not accepted by the church as canon, it teaches the following:
Let every apostle who comes to you be received as the Lord. But he shall not remain more than one day; or two days, if there's a need. But if he remains three days, he is a false prophet.
Paul stayed in many places more than three days.
And when the apostle goes away, let him take nothing but bread until he lodges. If he asks for money, he is a false prophet.
Paul said it was ok to be paid. He also accepted gifts from the churches.
And every prophet who speaks in the Spirit you shall neither try nor judge; for every sin shall be forgiven, but this sin shall not be forgiven.
Paul told us to check what the spirit says and if it goes against the word it was a false prophet.
If this is the case then Paul was a false prophet!!!!
Example like this are why Christians are very dubious of catholic "sacred tradition". So much of it contradicts Scripture when it is closely examined.
Didache /=/ dogma of the Church. The Church did not receive it as having the same always-and-everywhere authority as Scripture. It does constitute evidence of the concerns of the Church of that particular time and place.
We know (from Paul) that the Church in Jerusalem, as a result of a famine, and also persecutions which left some households needy because their breadwinner was in prison, needed help. Paul and Barnabas made an initial famine-relief visit to Jerusalem in A.D. 46 and delivered a monetary gift from the church at Antioch (Acts 11:29-30). At that time the Jerusalem church expressed the hope that the believers associated with Paul would continue to remember the Judean believers, which Paul was more than eager to do (Gal 2:10).
Possibly he church in Judea was also troubled by itinerant preachers who stretched their welcome in households which could not afford extended hospitality. The Didache says, "Cut that out." This is not expressed as a rule binding on the whole Church.
Same thing about accepting money: this is not presented as a doctrine or discipline of the universal Church.
As for prophets: you yourself noted that the author(s) of the Didache judged some people to be false prophets if they imposed on people excessively for money or lodging. Obviously they can't forbid judging prophets altogether: that's what they're doing!
Later on the Didache says not to judge "any prophet who speaks in the Spirit." So they would apparently agree with Paul that you have to check what the spirit says! and if it goes against the word it was a false prophet!
Do not get the universal authority of the Scripture confused with the possibly temporary, local, or lesser authority of other Apostolic-age writings, which --- although they are not universal --- still enable us to understand what the local Christians were concerned about.