Its not the best idea to put a rabbit upside down .I also have 2 lion heads and one is so fluffy that he's basically a mini angora. I use a wide tooth comb and set then on the table with snacks and I brush and pet then at the same time. I do it every seccond day and the brushing time is less and less. My trick for cutting out matted fur is to work your comb into the hair between the mat and the skin this way you won't cut their delicate skin as the comb acts as a gard. As well for getting their underside I have a friend sit on the couch and have the rabbit upside down between their closed legs and they hold them gently and pet their ears and cheeks. I only do this every couple weeks to check for mats and I try my darndest to not have them there long and usually they get some banana and cuddles after.