I apologise for not having tested this fully when I found it, but I can say that I have now. This skip requires that you go to DC after shopping and also requires you to do pickpocket after Memory Den. There appears to be a correlation between how quickly you move onto the next Nick oriented quest and whether he will co-operate or not.

What I currently do; Kill Kellogg Load Warp to Rocky Cave Leave Power Armour outside Rocky Cave FT to Park Street Do Park Street as normal Quick kill Dino with Frag Mine Quicksave (just in case) Talk to Nick (This initial dialogue appears to be essential to getting the skip quickly, spam E and Down, you want to trigger the skip dialogue as soon as possible so that you never really leave dialogue) Skip dialogue with Down Quicksave once gained quest Load Warp to Rocky Cave FT to Goodneighbor Run to Memory Den Enter Memory Den (If Irma says 'Well, Well Mr Valentine' then everything has worked perfectly) Do memory sequence Go to Rocky Cave (either load warp or FT, depending on if you run out of the memory den building or not) Talk to Virgil Collect Power Armor from Rocky cave FT to Sanctuary Talk to Preston Pickpocket Sturges FT to Goodneighbor and continue run from Railroad.

Be sure to let me know if you experience any problems with this. But after me testing this quite a few times this seems to work fairly consistently.