I'd also only heard it used specific to a journey, but just found this definition (the second group, from Collins http://www.thefreedictionary.com/schlep) includes:

  2. an arduous journey or procedure

I feel there's a connotation of unnecessariness to the difficulty ("clumsiness" in the literal meaning is similar; that it shouldn't be there). e.g. climbing Mt. Everest is "an arduous journey" - but I don't think it's a "schlep". Unnecessary difficulty is just the thing for a startup to target. Suffer that tedium so your customers don't have to.