Welcome to the J-Pouch Group, Kirsten,
I have to 2nd (or is it 3rd?) the replies from Bill and Janet. First determine if life where you're at can be improved... this is another major surgery with a great deal of risk. Any doctor who can recommend the surgery would also first need to determine if you were even a candidate as it's not an option for everyone. If totally successful, it is still provides another new, imperfect lifestyle at best.
You mention what you can/cannot eat. In general everyone's tolerance for certain foods and capacity to hold them improves with the age of the pouch and you are still in the relatively early years. Both the J & K are still "pouches" just with different "exits" so some problems can persist depending on the cause. Gas is worse since it can't be expelled without intubating. I eat a some things now that I hadn't, but there are new things that take their place so it's really a wash. All those lovely restaurant mashed potatoes with the skins mixed in, any dente vegetables or ones with hearty skins, leafy greens, hidden things in chunky mixes...all problematic for me. You will likely be surprised at what comes out undigested when you are face to face with trying to get it out through a Marlen 30fr catheter and its two very small holes.
You also mention pain when you can't get to a toilet or before you have to go. That could be due to a number of things, those Jan mentioned, diet, inflamed rectal cuff, rectal muscle spasms, etc, for which there may be a remedy. I also had some pain before, but nothing like what I live with now. I take pain meds for chronic abdominal pain and rectal pain, which both become even worse if I don't get to a bathroom regularly or even immediately after I've eaten something that upsets my K-pouch. I'd hate for you to jump in only to find that your pain doesn't improve, or that it worsens as a consequence of the additional surgery or new complications.
As for sleep, no improvement for me on that end either. I've heard some people with the k-pouch say they can go 6-8 hours without intubating, but I have to go at least every 4-5 hours. If you are still going 4-10 times every night, you should definitely follow-up with a gastroenterologist experienced with pouches, as that is understandably not good. In addition to diet changes or treatment for possible dysfunctions, you might simply be able to take medications which slow motility or thicken output. Your doctor should definitely want to determine the cause, either to find a remedy or to know whether the k-pouch would be a fix.
Lastly, when I had a J-pouch, I could technically use the bathroom whenever I wanted. I carried a makeup bag with supplies only because I leaked regularly and was always at risk of an accident when away from home. But now, I literally cannot use the bathroom without a catheter. They're not sold at the corner drugstore, at best it comes in two-days from a medical supply company. I have found myself 3-hours from home or farther on several occasions having forgotten my supply bag and immediately returned home in pain. I have also found myself in a public bathroom stall on numerous occasions unable to irrigate because I forgot a water bottle or had water but no syringe or enema bottle to get the water in the catheter. And forget about port-a-johns! Everyone is a little different, but you get the idea -- it's another major lifestyle change.
Reading postings from those with k-pouches on the forum would give you better insight into everything that comes with it. Everyone I know got a k-pouch because their J-pouches presented major health problems... enough so to warrant the risk of another major surgery with no assurance of lifestyle improvement. As for k-pouch or bcir docs, there is a list here on the forum people try to keep up. To date, I've never heard of a Kaiser doctor, but I'm not with Kaiser. Getting a continent ileostomy is not a common procedure -- we've got great docs in Michigan, but none with significant experience with continent ileostomies. I had to go to Cleveland Clinic to get help with my j-pouch and then eventually for my k-pouch surgery (a return to the ostomy bag was not a medically viable option.) I wish you the best of luck with your progress and hope you continue to find this group as helpful a resource as I have!