Dishes are out there and yes they will do ku and ka. Rain fade is a tricky thing. I honestly don't think you can eliminate it 100% on k band frequency's but a larger dish will make a difference.
Take my situation I only have SD so all I need is 101. I started with a 18" dish, then modified a Slimline, then went to my 90cm Old Primestar dish (which I currently use). I have lost the signal even on the 90 but its coming down in buckets when that happens. I had a pretty heavy downpour a couple weeks ago and I did not loose picture once. I was watching the signal meter and it bottomed out at 60. I normally run high 90's to 100. I think if I was on the Slimline it would have died and forget about an 18" So the name of the game is more gain to start with wins.
Getting back to where to get larger dishes you can try.
Global Communications
http://global-cm.net/
If you want to look at some monsters try here:
Vincor Limited - Earth Station Antenna and Satellite Communication Product Specialists
I know the VP of the company and he uses 5 to 6 foot dishes for Direct setups on the commercial end.
You could also look around your area and see if there are any Primestar dishes that are orphans, that you can get for the asking. Do a bit of modifications to the lnb support and your on your way.