Having owned a similar older 172, there is no way I would go through all that effort to install an O-320 when cost wise, the afore mentioned O-360 would be a much better option. You can always pull the throttle back and get similar fuel burn if that's your concern. Or full throttle to get that awesome TO performance. Resale with the O-360 will also be a huge plus. Yes, I realize many say they are never going to sell their plane. LOL, well, I had my 172 for just shy of 40 years before I sold it.
As mentioned, the cheapest route would probably be the already mentioned Airworx O-300 option. They have a FB page with dyno results. You retain that smooth running 6 cylinder and no issues with engine mount scrounging and other issues. I visited their operation a couple of years ago and had planned the conversion before deciding to sell my 172. If memory serves me, I'm thinking they dynod the engine at 174 HP. Only other requirement is a pitch change for the prop.
I did know of a guy that put an O-320 in exactly like you are asking. I say, did know, as I lost touch with him. He was a canadian that was living in New Mexico at the time.
Took him quite a while to scrounge the parts and in the end, he wished he had gone with the O-360 as the performance was minimal. He only did it because he already had the engine. He told me that he should have just sold it and used the 360.