If I'm understanding correctly, there are a couple of issues with what you're trying to do, which you may already be aware of.
First, your question says 'apply the same color ramp' but what you're really trying to do is apply the same color assignments as stated in the description. Whenever a color ramp is applied on classes, the assignments are random even if the same color ramp is used. The only way to get them to match up is either use a lyr file/import symbology from one or set them manually in both. And to clarify, saving out a lyr should preserve everything and not reset anything - however importing it will change the target line symbol to whatever type is stored in the lyr.
Second, depending on how your arrowheads are created, there's no way to have them match the color of the line without setting it manually. This is a long-standing issue and may already be a feature request. You didn't say if you needed them to match or not, but if so doing it automatically with a color ramp is an additional complication that requires using a multilayer line type and doesn't necessarily get the arrows at the ends.
Finally, there's a problem with the way lyr files and 'properties for all symbols' (and similar dialogs) work in Arc. In some software you can select which properties to change, but with Arc if you want to change one you have to change them all. If you use that menu to add your arrowheads, it will also assign the same color/style/etc. to every class. In much the same way, if you have one class symbolized one way in a lyr file and want to add that to an existing symbology, you have to do it manually because importing the lyr will overwrite all other classes as well.
In short, I don't believe there's a way to do what you want without manually setting either the color or the arrowhead presence for each class as global application of one will reset the other.