the cheapest way to convert your money into Bitcoin or vice versa is by doing it with other users.
no matter where you go every market or platform will charge you a fees for every transaction,
they're charging you a fees for doing a trade and then transaction.
it would be best for you to find someone from your country or someone who has a conversion target,
in this forum you can find people who want to sell or buy their Bitcoin to other people directly,
try to reach them and make a deal,
you only need to pay the fees for transaction from your wallet to other wallet,no more than that.
go here for your reference :
https://bitcointalk.org/index.php?board=53.0[
Currency Exchange]
Also, would it be smarter to convert the BTC to LTC or ETH (only other currencies supported by Coinbase) and then sell and have sent to my account?
No it's not,
it will only take you more fees from before.