There is a known issue with the Duty finder freezing when taking a full party in - there are several other posts here with the same issue and it is yet to be fixed.
If you are a DPS class soloing, then you have to deal with long queues i'm afraid. Amdapor is technically endgame and one of the tougher dungeons, with many Linkshells and Free Companies choosing to farm with people they know as opposed to taking the random gamble.
You can try setting your language and country settings in the duty finder to include JPN and non-English speakers as this may help your queue times - the Duty finder is cross server so this delay is conclusive across the board...
You will likely find the same with Wanderers Palace/Hard mode Primals.
Sorry to be the bearer of bad news...