New main cables for a suspension bridge

This thread discusses the sheer difficulty of replacing the main cables of a suspension bridge, that is the cables that go over the towers and that ultimately support the bridge:

The general consensus in the thread is that replacing the cables would be extraordinarily difficult, and as I’ve thought about it, it seems that probably the most cost-effective thing to do if the main cables of a suspension bridge need replacement would be to just build a new bridge. But let’s say that that’s not something people want to do because the bridge is famous, such as the Golden Gate Bridge. So, using that as our hypothetical bridge, how would it be possible to replace the main cables?

Just for this hypothesis, assume that you can close the bridge to traffic for as long as you want, and that money is not the biggest factor, but try to keep the cost under double what a new bridge would probably cost.

My idea, and someone else mentioned it in the other thread, is to put up some falsework under the roadbed, remove the old cable, install the new cable, hook everything up, and remove the falsework. In other words, pretty much the way they’re building the signature span of the new bay bridge (although that is not a suspension bridge). Is there anything more feasible? Is putting up temporary supports in the Golden Gate even that good an idea? I don’t know if the seabed is all that great for that sort of thing. I also have no idea how much this would cost.

The link in Meurglys’s post in the other thread looks like a good start. In it they discuss several options for new cables over or alongside the existing ones. If you absolutely need to replace the existing cables, make those new cables temporary, while you remove then replace the old ones.