As others have said, try Germany, Belgium or France for cheaper accom. All well connected to Findel by motorway, and if these get busy during rush hour, well, that's "busy" by LUX standards. And do remember to fill up this side of the border
Since the A13 Motorway has opened, the Moselle valley is definitely worth a look. On the German side, EUR 1500/month will take you WAY further than a 3 bedroomed flat in the Moselle valley (come to think about it, even EUR 1000 probably will ). Trier is more expensive, but still much less so than LUX itself. And then there's France - very nice for families as the French tax system works in their favour.
Oh, and Arlon (Belgium) is a dump IMHO. Don't even think about it. Even Longwy (in France) is nicer.