32X solves it all. No slot cutting, no game genie code screens at start up, and has a slot big enough to fit the Jap MD carts.
So to rephrase an earlier post: Get your hands on a 32X and dive into all that Japanese goodness!
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But you might as well get a Game Genie anyway for games that you do need lockout codes for.
Eliminate Down is a mix bag. It has some really impressive and fantastic looking levels, then it has some really mediocre levels. Not that other shmups don't have that kind of design mixture, it just feels exaggerated in Eliminate Down. I dunno.
Glaylancer is a solid game all the way through. The game itself it great and solid from start to finish. It also has that original 16bit feel to it, if you're more into that side of the 16bit generation (which I am). I highly recommend getting this shmup. You won't be disappointed.
I'll give you the 99 ships cheat, but the rest of those don't really have any effect on the game itself. You don't play the package art, and regardless of what they called it over here it's still the same game.
Now I can see picking up the Japanese version of say Dynamite Headdy or Contra Hard Corps over the US equivalents, but this strikes me as a case where it really doesn't matter. And I think the "benefits" you listed would be outweighed by the fact that you would have to enter a game genie code every single time you wanted to play it. Just my opinion, of course. :)
TL;DR version: Just get Lightening Force, OP.
It basically only comes down to whether or not you're anal about not having the misspelled "Lightening" or not.
I don't know why you would buy Tatsujin over Truxton either since I think you can trick the game into playing as Tatsujin if you really want.
I like to spell it lightening thunder force 4.