How (un) reasonable is to take the ratio of GDPs in local currency over GDPs in USD to convert ... to current USD?
That will not convert them to current USD prices. So it is about as reasonable as dividing any random two numbers.
The way how to convert them is to use either use exchange rate or PPP. PPP is better for international comparison than exchange rate since it controls for geographic differences in price level so I would suggest using that unless you just want to convert the values without such adjustment. Since you want current prices you want to pick exchange rate or PPP at the same time period and you want to avoid making adjustments for inflation.