In 2005-6 when the US was engineering the Hamas-Iran alliance of money and influence, there were warnings that Hamas would become more hardened with Iranian money and influence. Shia Iran and Sunni Hamas were not natural allies. All three of the countries under consideration are more moderate than Iran and might have a moderating influence.
Australian police arrest 5 over shooting 'linked to terrorism' (Reuters)
from the article: Turkey may provide Hamas with $300 million in annual aid