I've worked with Kona solids, and yes, some have been easy to quilt and others hard.
You can make it easier for yourself by keeping the quilt sandwich tension fairly loose, and quilting on the bias instead of on the grain - there's more flex that way, which makes it easier to rock the needle. Also, try different sizes and brands of needles...some seem to penetrate better than others.
I have no problem using cotton batting like Mountain Mist Blue Ribbon, but you might find it hard to quilt. So, you might choose a poly batting like Hobbs Polydown, or if you like thinner battings, Mountain Mist lite or Hobbs Thermore. Quilters Dream in the lightest weight is also a possibility. It may be worth experimenting a bit with sample sandwiches with different battings. Harriet Hargrave sells batting swatches in 15 inch squares, which are great for testing.
I also use muslin backings, mostly because I'm afraid to use regular quilting weight cottons, in case they make it harder to quilt.
Good luck - I hope you post pictures.
Janet