Last I checked, Bluehost does not use cPanel, so they will not do the migration, as it is a complete headache to migrate either to or from them. Not sure who is actually recommending them (you aren't using one of those "Top 10" sites that they pay to be on, right?), because they are a horrible host, and owned by EIG (Endurance International Group), which is the same company that owns Hostgator. Same support techs, same servers, etc. So if you're not happy with Hostgator, you are most definitely not going to be happy with Bluehost.
Softlayer, as far as I'm aware, do not provide managed services on their cloud or dedicated servers. So no, they aren't going to do it. No unmanaged provider is going to help you there.
You are correct about Knownhost...you have to buy either a VPS or dedicated server with them.