If you tested the 'stat, it is open by 160*, correct, and you're sure the raw water pump is good (including the wear plate, if this is scored even a good impeller won't pump properly) then the next thing I'd do before replacing the whole exhaust system is drain out the water and remove the exhaust elbows to see how clogged the passages are in the manifolds and elbows. Sometimes you can rod out the passages in the manifolds and re-surface the mating surface and just replace the elbows instead of the whole system, but it can be risky. I do see rust seepage at the joint between the 2. Volvo had trouble with the original gaskets and revised them and published instructions on how to properly resurface the mating surfaces. 180* on your stat housing and exhaust elbows or manifolds is definitely too hot. I have an old '88 OMC Cobra and the impeller is different but the rest of the system is just the same as the Volvo, and the stat housing (top part) will be about 135*, the intake manifold right below the the stat housing will be about 145-150 and the manifolds/elbows will be between 95-110 at idle, the hottest they get is about 135 and that's only after coming off plane, they will cool off pretty fast after idling a while.
If you haven't done it, make sure all the passages in the stat housing are open, these will get restricted with rust just like your exhaust system and if you don't have good flow to each manifold they will for sure get hot. Just rod them out with a coat hanger wire.
The other thing unmentioned here is the path of raw water on the engine, you can have clogs in your water intakes on the outdrive, not common in fresh water I guess it but is here in salt water (marine growth), there is a copper tube that transfers water from the lower unit to the upper unit and the grommets for these can wear out/soften and then you don't get full water flow to your impeller. I would test the output of the raw water pump and see if you're getting what you should in terms of volume. If the grommets for the water tube are leaking internally then you have to split the drive to replace them.
If you have to replace the exhaust system do NOT buy off brand stuff from Amazon, if that joint between the elbow and manifold leaks because of poor machining of the cast iron you will have water in your cyls and a possibly ruined engine. People used to have a lot of trouble with GLM exhaust because of this, they might be better now, but I heard bad things about them from a marine mechanic I know well and a guy I get my parts from won't even order them. The only aftermarket I'd use is Barr Marine. I installed a set on my Cobra 8 years ago and they are still good (this is good for salt water use!) and it all fit right with no leaks. And you definitely should check the flatness of the mating surfaces with a straightedge and feeler gauges (less than .003" variation).