score:3
There are trains to Schiphol every hour through the night, it's the Heerlen end of the trip that make it difficult. So you could first go to Utrecht, sleep there and catch a train in the morning. Or go all the way to Leiden or Amsterdam by train on Saturday afternoon and take a train, bus or taxi on Sunday morning. Depending on the type of accommodation/level of comfort, it should be possible to find cheaper ho(s)tel or B&B in those cities than at the airport. You would also have more time to sleep in the morning than if you were to take your own car or a long-distance train during the night.
Upvote:3
Sleeping in the airport should not be a problem. Your situation is not uncommon at all. The need to spend the night at the airport either for early flights or connecting flights happens. There is even a website dedicated to this subject with tips regarding the policy of the aiports about people sleeping and the best places to do it.