1. I agree with others, 6x and 7x is just ridiculous for steelhead. I typically use 3x and will go down to 4x if necessary. Beyond that, yeah, it may help you hook up more often, but you'll lose a lot more too and its just not worth it to leave hardware in all of those fish. I've heard of people using 5x, though I wouldn't do it. I've never even heard of anyone using 6x or 7x. I won't use 7x on regular sized trout!
2. If the tippet is mono or copolymer, then actually, a LONGER tippet will help protect it, assuming you can keep it from twisting up, which weakens it. Mono stretches, so having a longer length is like a shock absorber. Same idea as a soft rod tip, which also helps a lot.
3. Keep your drag set light.
4. I'm generally not a proponent of flourocarbon. And yeah, it has no stretch, so in using it, you lose that shock absorption factor. But I do often use it in steelhead fishing. I think this might be one instance where fish actually become line shy, where flouro is an advantage, rather than drag shy, where its a disadvantage. If it allows you to go with a larger tippet, say 4x, then that extra strength will more than offset the shock absorption penalty and is well worth a try.
5. If your problem is the line not fitting through the eye, first, I've never seen a hook that 6x won't fit through, so that still wouldn't explain 7x tippet! And second, there's a pretty good variety of hooks available, I'm sure you can find one with an oversized eye to tie your midges so that you can get 4x or 5x through.