sounds like you haven't got the miter box setup properly if you are using the stew mac one, the brass blocks need to be right up against the side of the saw, i have to use general pupose white grease to move my saw thru the miter box i keep my saw that tight, i also don't use the brass blocks for depth at all, so lower them as close to the teeth as you can but still be able to get the blade in and out for the box, that along with tightening the blocks to the saw will help prevent any twisting of the saw (the butterfly slots you mentioned)
use a peice of a coke can or some little peice of thin metal and score a mark for your depth to check the slot depth that way ( much more accurate then a pencil or pen mark on paper)
once you have the saw lubricated in the box it should fly thru the wood, unless it's an old saw, then you might just want to get a new sharp one, or if it's still getting "stuck" in the wood, definitly try scott's candle trick, or pick up a can of dry coat it's a tool cutting edge lubricant
that's how i had my box setup and i can slot a board in under 30 mins.... but i do have pretty strong arms
EDIT: woopse, you're using the saw free hand, ok, well buy the miter box and the fretting template... then follow the above... the box will easily pay for it's self in one use by the sounds of how long it's taken you so far (no offence intended)