Some really helpful reflections here. Mikey Lynch picks up Phillip Jensen's comments in The Archer and the Arrow about how to avoid "making the gospel just one central part of the Bible on the one hand, and not making everything the Bible says the gospel on the other."
The gospel is likened to a circle because it's various elements ('arcs') are not only interrelated and interdependent, but self-reciprocating. And "for any true circle, one arc of the circle implies the whole."
So sin following creation leads to judgment because God is creator. And his judgment teaches us about what it means for him to be the Creator. And it teaches us what sin really means. And it also teaches us about salvation. And judgment leads to salvation because God is the judge. And salvation leads to new-creation.
Mikey I think your questions are important:
"If I just preached these arcs would they necessarily imply the rest of the gospel?" and "If I just preached these arcs, would I have preached the gospel truly, even if not fully?"
I think if we preach each arc properly without going beyond it we are preaching the gospel. Because as we teach that God is creator and judge, part of what we see when he brings his judgment is his commitment to creation, and his faithfulness to himself resulting in his ongoing grace and his purpose to bring renewal to creation - which is the message of the gospel.
Again if the arc we're dealing with shows the sinfulness of people, that same arc will bring out the righteousness of God more clearly, leading to him revealing his righteousness - which is the message of the gospel.
So each arc contains the same direction looking both forward and back as all the others. I think sermons can be the same: a sermon on judgment can contain the same forward and backward perspective as one on salvation, and give the gospel message on its own.
One test of this is to put ourselves back in to the shoes of an OT preacher, say Noah, and ask if we can still preach 'his gospel' today in a timeless way. He was a "preacher of righteousness" in his day. And the Ark (not intended pun) was a massive visible word-picture to his generation leaving them without excuse. As Noah spoke to people about what God was going to do and what he, Noah, was doing with the Ark, I think he was preaching the gospel - a message of good news for those who were being saved, and a message of bad news for those who were not.
Now of course if we today preach from that time in salvn history and stay on that arc re. sinfulness and judgment, when we apply it to people today with a correct understanding of what it means in a timeless sense and in a relative-to-now sense, I don't think we need to simply put '2 ways to live' over the top of it in order for it to become the gospel.
But by explaining to people fully what God did there in the past (Noah's time) and what that means about both God and us in a timeless way, I think we are not making a jump to appealing to people straight from that to repent and turn to God in faith. I.e. we can 'herald' the word of the gospel right then and there without a full exposition of Jesus' work on the cross to make their forgiveness possible.
Of course know that we can do that because of Jesus' coming, but because it's always been possible prior to Jesus' coming, there is this timeless element to the gospel in the Old Testament and throughout Scripture. Rahab's conversion with the spies prior to the judgment at Jericho is a classic example of course.
I'm not wanting to advocate for permission to cease making forced references to Jesus as a 'tack on the end' simply by leaving out Jesus altogether and worse forgetting the centrality of God's eternal plan for the cross and the natural climax of it in the unfolding flow of the Bible narrative.
I guess I'm just trying to reflect a confidence that I think it is possible to both at the same time preach the gospel truly and do as Jensen says, 'not preach the entire circumference of the circle, but just the arc(s) of the gospel that God puts in front of us in the passage.'
Or is this what you mean by "making everything the Bible says the gospel"? If it is, then I reckon it's fair game. Don't we want every sermon to be a heraldic exposition of the gospel from any and every part of Scripture?