As the owner of a dual arbor 16 inch saw in a two car garage shop, I can definitely state that a 12" isn't too big. As long as it fits in the space you have available, there is no reason not to get a bigger saw. Generally speaking, saws that accept larger diameter blades have heavier castings, and generally run smoother than smaller saws.
As far as phase conversion or new motor, You have four standard options.
1. Get the power company to send 3 phase power to your shop. This may or may not be a possibility and can range in price from (almost) free, to ridiculously expensive. It's probably worth a telephone call to find out though.
2. Buy a VFD. Single phase 240 to 3phase 240 5 hp VFD's are easily available, but probably more expensive than you would want (I'd guess about $800.)
3. Buy or make and RPC. I would personally suggest making one, but your comfort level may vary. You'll need at least a 5hp 3 phase motor, and enclosure, and a variety of capacitors, etc. This is probably you're cheapest option, and it has the added benefit of opening the door for other three phase machines.
4. Buy a 5hp single phase motor. Depending on the source, this price can range from 300 to over a 1,000. You'll need to find out what mounting base your current motor has. In addition, 3 phase motors are generally smaller than single phase motors of the same HP, so you may have difficulty getting a single phase motor to fit. However, I have no experience with your current saw, so that may or may not be an issue.
Please let us know which route you choose, and how everything ends up.