Unbalanced to balanced variable impedance matching
You say "frequently the impedance mismatch caused much pain" - that is odd. Any half decent console output will have an output impedance around the 50-100 ohms range, and you should not be presenting a load that looks like less than 10k or so. If you are having problems in this situation, it is more likely that : 

(a) the connection is balanced and you are sticking an unbalanced connection onto it, which could make the other connected inpuit level suddenly drop by 6dB, or ...

(b) you are running into grounding issues in an unbalanced system (these are all too common, and they can be a bit fragile). 

However there is a reason that old school pro (read : broadcast) consoles insisted on good quality transformers all over the place, and that is that they were frequently connecting to equipment which they neither knew nor trusted. Transformers have the great twin virtues of providing galvanic isolation (goodbye grounding problems and hello to not worrying about badly behaved systems or electromagnetic phenomena blowing up your gear) and being capable of being connected to balanced/unbalanced gear more or less freely.

So if you are frequently in this situation the nice thing to do is (as suggested above) to respect your hosts system and have some boxes with good quality (e.g. Lundahl/Sowter/Jensen) audio line input transformers (the input side connectors to the host, the output to your gear) and a variety of connectors (which just saves a bit of hassle).

(This would have been a comment but a bit too long for that.)