I understand the pain of not having a bandsaw. Even a tabletop 14 inch model would allow you to saw those limbs.
How long are the pitman arms you are trying to make? Because if they are not too long I'd also look at splitting with an ax or better yet a froe. Splitting goes with the grain, which is stronger than sawing where you could get areas where you're cutting across the grain.
If you manage to split it, then you can run it through a planer to make it nice. I'd also say don't have the heart in your pieces.
If you can find somebody with a bandsaw, that would be easiest. Or better yet find a sawyer that can just provide you some hardwood boards.
Here is woodmizers sawer locator:http://www.woodmizer.com/us/ResourceCenter/FindaCustomSawyer.aspx