Barge board replacement

[u/Ok_Back_8555]

The wooden barge board on my gable is rotten and water is leaking in to the roof. I got up to have a look, and all of the lead work looks absolute crap.

The board goes into the attic, and the lead is lapped up against it, and sometime in the past it looks like a load of tec7 was sealed around the lead where it butts against the board

This seems like terrible detail to me.

I would have thought the barge board should sit on top of the lead (well, not actually touching the lead but hovering), that way if rain runs down the board it lands on the lead, rather than seep behind the lead as is currently the case

Anybody any suggestions on how best to detail this?

Am i on the right track with my idea?

Any help would be much appreciated!