okay dutch man is a flaking system, it has nothing to do with the stays, the stays are what hold up the mast.
i could be wrong but what i see your setup is:
from what i see the cable coming off the top is the topping lift, it holds the boom up when the sail is down. yes the dutchman system attaches to the topping lift. the main sheet in the line that you use to pull the boom in to get it where you want. now the tooping lift used to connect to the broken fitting on the rear of the boom ( top broken loop ) and the main sheet attached as it is to the bottom of the fitting. the fitting rotates on the boom, this allows the boom to rotate and have the sail wrap around it for reefing. at the front of the boom it should also have a swivel type fitting that is probably screwed in place so it cant rotate anymore.
the topping lift is now attached to the boom where i would think the out haul would go. which should be fine, but you need to find a way to securely attach the main sheet, either by replacing the fitting that is worn/broken or by a bail thru the boom. using a bail is probably the cheapest way, as they cost 15 bucks each. then you can do away with the rotating fitting on the end on of the boom. you could also get a "strap" to go on the bolt that holds the swivel on and have the main sheet pulley/block attach to it