I started the quest and wanted to increase the effectiveness of the crossbow as fast as possible.

The problem is, that when I'm supposed to pick up the enhanced crossbow schematic from a chest in a "random" cave, it simply isnt there. I found the player.additem code for the schematic but it doesn't continue the quest even if I have it in my inventory. I also tried storing the schematic in the chest to pick up afterwards, but then it just disappeared.

I need help for this, its kind of ruining my experience.

http://www.uesp.net/wiki/Skyrim:Ancient_Technology

to move quest by console:
sqs DLC1RH05 - Lists all stages of that quest and shows if a stage is achieved
setstage DLC1RH05 XX - XX is is the number of the stage you wish to complete

If some resons any quest bug you can repair it this way. If UESPwiki or Skyrim wiki dont know quest ID you can always find on your own just write sqt in console - List quest ids and targets(Page UP, Down to check list)
Hope this will help you

Thank you so much, it seemed I could do much with console codes.