Did a nice thing today by contacting the regional office of Goodyear on JC Road. Although they don't have a retail store there, they were really helpful and also told us that they can get the exact same size (165/80R13) that the Palio needs and that they have the tubeless version as well. So that's like one issue solved. It may take them up to 2 weeks to get the tyres, but now that the exact size is available, I'm fine with waiting :)
A special thanks to johnm for his tyre related advice on IRC and his idea to contact the manufacturers.
And no obz, you're not the only one who finds the Universe much more interesting :)