As this got resurrected I thought I'd add what is helping me most,
I have saved aspects by working out, before doing anything, which runes only appear 2 or 3 times - they will be the ones you need for the piece of research, I dont light up ANY runes till I have moved any blocking rubbish runes out of way and moved the rare research runes into position, This means I only have to use 1 aspect of each type to light and join them up. Obviously it helps if you know what aspects the research takes, cheat sheet or previous experience of TC helps, but even if you are guessing what aspects are in the research, this method will save you aspects, as once you find the correct aspects they will all join up and never need to be turned off. Sometimes the rubbish ones need moving to block shortcuts that the game makes between runes, no cost involved. All it doesn't save is time as you still have to complete the puzzle,
hope this helps and that I've explained it clearly, I know its made a big difference in my research.