Or simply start with ethylbenzene? I'm presuming it is cheaper than styrene.
Surprisingly EB is currently ~30% more expensive than Styrene. But same ballpark. 30% isn't huge. Yields etc. might easily make up for that.
Process chemists can probably answer this better than I, but sometimes a price can be higher due to a lack of demand, a reverse of why styrene is so cheap. I wouldn't expect a lot of people buying ethylbenzene just to make their own styrene even if the price were less. I think this is where you can begin to learn chemistry. If you begin with bulk prices and apply processing costs and yields, you can understand the cost of goods. If you are thinking of production, you can also step back to benzene and calculate ethylbenzene from there.
I would also suggest checking the patent literature more carefully. I would be shocked that I could suggest a patentable route in a chemistry forum wondering about alternate routes to a potential commercial product. I don't know this, but I'm not going to hold my breath waiting for anyone to contact me for my signature on their patent application. It is a lot more likely someone thought of this way before me.