I'd take the earliest flight to GIG that I could. As long as you've got 4 hours at a minimum I think you'll be fine. The Star Alliance lounge they have is new, quite large, never busy, and very, very nice.

Flown thru there with and without checked luggage over 100 times myself.The bag smashers are notoriously slow IMHO. And, I expect airport security to he ramped up significantly (which means it will get slower) due to the expected anti-corruption/drug trafficking position of Mito's new government.