I've seen this problem with hoses draining dehumidifers (not even trying for a trap as thethey drained into a channel drain.) They would back up 10 feet above the dip in the line if the line got a dip in it.
I think it comes to lack of venting and the small diameter of the hose. If you put an air gap/standpipe and P-trap (of some normal diameter for drain plumbing) for the straight sloped line to drain into I think that will solve both sides of your problem.
Depending what you have available, draining into a sump pit is another approach to not have it dripping down the side of the house.