How is this going to work now?

I speculate it will only work via manual activators that can be built in settlements.

It could be potentially more awesome than the original method if said activators could be used to travel directly to each other, rather than stopping to—you know where—first.

The easy method would be that you can only fast travel to there. The problem is where do you go when you leave. If you can fast travel to any location from that place, then the whole point of no fast travel is rendered pointless. Of course, it is possible that a new item will be added to your inventory so you have to activate it to get to that location and to your previous location.

I scrapped that initial item.

but that's the way they could do it.

Rely on the initial item that enables you to go there, which you can only build one of, but are able to move it to another location if you want to.

Alternately they could put in an elevator.

To leave "that place", probably take the elevator back up to the arrival platform you see when you first visit, and use that device there. Probably would allow you to go to Home Base only.

Or, you can fast travel in freely, but you can only fast travel out to the same point you came in from.

Or, it'll be the only way to fast travel like that and it'll be a nice convenience for people who make that decision.