The ZX10/Ninja 1000 most likely has Keihin VG38 or CVK38 carbs; nothing special about them, really. There is only one gasket that may need replacing, the neoprene 0-ring on the float bowl - they're probably OK.
To start by addressing the carb swap - unless you know what you're doing this will take a long time, be frustrating and expensive, and have less than optimal results. For starters, the jets and needles will be all wrong, the geometry in the frame (the carb holder) will be all wrong, and you'll need to put the four carbs from the 9R into the 10's rails. There may be issues with mounting hardware, holes, screws, throttle linkages mismatched, etc. The rubber boots used to mate the carb throat to the cylinder head may not match.
I think you're better off fixing your carbs.
The symptoms you describe sound like a lean condition. This can be caused by the vaccum diaphragms leaking, slides sticking, emulsion tube clogging, or poor emulsion due to airjet clogging, incorrect needle height or wrong needle, wrong main jet, or vaccum leak between carb and cylinder head.
Before you go further, you should check the valve clearances, because open valves will have you chasing your tail when you try to fix carb issues. Next be sure the fuel filter is not clogged, and there is enough fuel flow to the carbs (take off the fuel line, open the petcock, with a small jar in hand to catch the fuel, and look at the flow. If it trickles...there's your answer, or part of it).
Then, if your problems still exist after setting valve clearances, take the carbs off the bike and disassemble them, and inspect them. There are some good websites out there on how to do this - do a google search. Note the needle clip position (if the needles are adustable). Don't take the carb bodies off the framerails.
Check to see the floats move freely. Check the float height - should be consistent with all four carbs. This is not the easiest measurement in the world to make, so google on how to do it properly for motorcycle carbs. I'd do the google for you, but I'm late for work.
If your inspection shows wear, or blockages - use a short peice of 10 lb test fishing line to poke throuugh the air passages to test for blockage - soak the parts in solvent for a few hours, and blow the gunk out with air or freon.
Sudco or Kawi should have the slide/vaccum diaphragm parts if they're torn or cracked, otherwise leaking, or scarred so they don't slide freely. I really hope your problem is just varnish on the slides keeping them from picking up.
When you reassemble the carbs, careful you don't crush the diaphragm cover at the screwholes - making depressions here with the screws will cause you vaccum leaks and not let the slides pick up like they should, starving the bike for fuel. In fact, look for this, if someone's been in the carbs before you. This can be fixed by using a light hammer, a 3" socket extension as a peen, and the flat part of a vice as an anvil...
One last thing - replace the phillips-head bowl and diapragm screws with allen cap screws.