As far as I searched for my specific travel dates, IST-FRA-ATL on Lufthansa Y is almost €400-500 cheaper than all airlines's IST-XXX-IAD flights where I intend to buy an American Airlines ticket for ATL-DCA. I have the option to have a 2h30 connection or a 5h one, if I choose AA Y ( would be Main Cabin Extra for free ) for the next leg. ( AA is my top priority because I will 2 have 2 checked bags which would be free for me depending on my OWS status ). The other option is to buy Delta First ( which has a $80 difference than DL Y which would waive 2 checked baggage fees); the Southwest ATL-DCA schedule does not fit to me and DCA would be my preference as I would pay more if I choose Spirit to BWI buy paying extra transportation + 2 checked bags + a carry on. I don't consider UA to IAD as an option.

So If I want to do something like this, how much should I allow for a passenger responsible transfer. Would 2h30 mins be fine or minimum 3h30 mins or maybe more?
I am considered as a Visitor and my visa type does not allow kiosks, mobile passports, Global Entry etc... so I must clear immigration at a staffed desk.

Thanks in advance;