Yes, fixing it at the source with Reshade is the correct approach. The display should be left in HGIG mode whenever possible.
Actually, even if the game outputs up to 10000 nits, it should still look correct in HGIG mode on an 800-nit display...
HDR10 static metadata is reliably sent only by Blu-ray players. I'm not aware of any other sources which can be trusted to always send HDR10 static metadata. LG TVs will use the 4000-nit curve for these sources, wasting most of the peak...