In all honesty, when I read Scripture I do not get that ‘salvation’ has anything whatsoever to do with a ‘Gospel system’ or ‘obedience’ thereof.
Surely you cannot mean that our deeds and works can make us righteous or clean in the eyes of a perfect and entirely Holy God? Moreover, we cannot follow any kind of a ‘system’ or formula, regardless of how good it may be.
Agreed 100%. There is no action we can do that can merit salvation, or make us good enough for God to afford us Righteousness. Just as there is no act a person can do to make a 1/4 cup bottle of oil pour out enough oil to fill every jar, cup, bottle, bowl, bucket, or other container that we own or can borrow from every friend we know. Yet, that is what happened to a person because of her faith in the prophet who commanded it. And if she could have borrowed more containers, the oil would have poured until those were full too.
That is what salvation is like. We cannot do it ourselves, but God can, and He will, if we obey His command. The widow in question would probably have not had nearly enough oil if she had not borrowed the containers as instructed. But she did, and she filled all of them with oil. We will not receive the declaration of righteousness if we do not equally obey God's command to repent, and confess Jesus, and be baptized.
Only Christ and His completed sacrifice, once for all, can save those who believe in Him, His Word, and His Resurrection.
Again, this is true. The question is, How and When is the righteousness resulting from His fully completed sacrifice applied to each individual. And the answer to that is: Exactly when Scripture says it is (Col 2:11-14, Rom 6:1-4, 1 Pet 3:21, Mark 16:16, Acts 2:38, Acts 22:16).
I think the most simple and direct quotes on how Salvation is ‘achieved’ (really awarded is the better and most accurate word) is from Romans and Acts.
So faith comes by hearing [what is told], and what is heard comes by the preaching [of the message that came from the lips] of Christ (the Messiah Himself). Romans 10:17
34 And Peter opened his mouth and said: Most certainly and thoroughly I now perceive and understand that God shows no partiality and is no respecter of persons,
35 But in every nation he who venerates and has a reverential fear for God, treating Him with worshipful obedience and living uprightly, is acceptable to Him and sure of being received and welcomed [by Him].
36 You know the contents of the message which He sent to Israel, announcing the good news (Gospel) of peace by Jesus Christ, Who is Lord of all—
37 The [same] message which was proclaimed throughout all Judea, starting from Galilee after the baptism preached by John—
38 How God anointed and consecrated Jesus of Nazareth with the [Holy] Spirit and with strength and ability and power; how He went about doing good and, in particular, curing all who were harassed and oppressed by [the power of] the devil, for God was with Him.
39 And we are [eye and ear] witnesses of everything that He did both in the land of the Jews and in Jerusalem. And [yet] they put Him out of the way (murdered Him) by hanging Him on a tree;
40 But God raised Him to life on the third day and caused Him to be manifest (to be plainly seen),
41 Not by all the people but to us who were chosen (designated) beforehand by God as witnesses, who ate and drank with Him after He arose from the dead.
42 And He charged us to preach to the people and to bear solemn testimony that He is the God-appointed and God-ordained Judge of the living and the dead.
43 To Him all the prophets testify (bear witness) that everyone who believes in Him [who adheres to, trusts in, and relies on Him, giving himself up to Him] receives forgiveness of sins through His name.
44 While Peter was still speaking these words, the Holy Spirit fell on all who were listening to the message.
45 And the believers from among the circumcised [the Jews] who came with Peter were surprised and amazed, because the free gift of the Holy Spirit had been bestowed and poured out largely even on the Gentiles.
46 For they heard them talking in [unknown] tongues (languages) and extolling and magnifying God.
Acts 10:34–46
If these were the only passages that mentioned salvation in any way, I would agree with you. But since ALL Scripture must be equally considered, we must not leave out passages like those listed above. There are physical actions that are REQUIRED before salvation is received (Rom 10:9-10 is one example), and every one of them must be fulfilled. If they are not and salvation is still received, then some Scriptures would be made into a lie.
For example: if salvation is received when a person simply believes (as John 3:16 states), then Rom 10:9-10 is made into a lie (because it says that salvation is received as a result of confessing with the mouth that Jesus is Lord). But if salvation is received just on the basis of repentance and belief, then Acts 2:38, Acts 3:19, and Mark 16:16 are made into lies because they place other conditions on the reception of salvation. All of these conditions must be met, or Scripture is not fulfilled.