Just to clarify, as I understand your question you want to turn your 2 1/2" thick slab into two slabs that are each the same size but 1"+ thick?
This operation is called "resawing". Typically this would be done with a bandsaw, however most home-shop bandsaws max out at around 1' of resaw capacity. For your slab you will need something with a much bigger capacity (30").
- You could find someone with a proper milling bandsaw, such as a Woodmizer. This is probably the easiest thing to do if you're really intending to do this just for one slab.
- You could put together a chainsaw milling setup (also know as an "alaskan mill"). This would get the job done, but I wouldn't be surprised if you end up spending $500-1000 if you don't have a chainsaw already. You'll also lose a lot more to the saw kerf compared to a band saw.
- You could attempt this with a handsaw, but it will be a lot of effort, and I think you'll have trouble keeping it tracking straight in the center. Most panel saws max out around 26". Working from both sides you might be able to get through it with this, but it'll be difficult.
Also, you should expect to have some wood movement after you resaw. This will probably cause you to loose a substantial amount of thickness when you go to flatten the two new slabs. It is entirely possible that you will not have a usable board after it's flattened.