Hi,
what is common is corrosion in water port jacket and it works its way to cylinder, the Head Gasket Breaks and allows water into cylinder "cyl 1 on mine"..just to repair that part cost me $200 Welding at Machine shop and that's cheap,then Machining head"if head is not too warped from overheating".
if head overheat too much you might as well go new 2nd hand good head as its been comprimised "weak" in Alloy..
then your Mechanic needs a gasket Kit, another $150-.And if Head Gasket allowed water and oil to mix.."usually resivoir runs out of water and oil stick gets way full" Steam out of Exhaust another tell tail sign.
A LOT of Cleaning oil sludge internally "means all 2pans off and cleaning/blowing/.
now with The head, if it overheated too much it might warp, usually means a new head, 2nd hand $450-..on assembly and dissasembly Both cams must come out to get access to Head Bolts "another $50-" in new + "more Labour costs".
then on mine i found "egr Valve,Vacumm Modulator, vacuum bracket all non functional, was it the faulty head over time?,who knows, but another $350+ , while in there might as well do timing chain, another $130-+labour.
so ill stop here as you can see every step costs money and that is not including mechanics Labour costs @ usually $70-$100 an hour..
so far i have spent total working hours 15, complete strip down and assembly..not finished yet as im waiting for spare parts from Japan.. so i would say $1600 is minimal work done to your car and a lot of luck..