I’d build the EF to 4–6 months first then channel the rest to a separate down payment fund; extra to the loans won’t lower your DTI because the minimum payment won’t change, while bigger cash reserves can help approval and reduce PMI. Keep the savings in a high-yield account and make sure the down payment money is “seasoned” for at least 60 days before you apply. Also turn on autopay for the federal loans to get the 0.25% rate reduction, and if you still want to chip away, send small principal-only payments as noted.
I treat it like changing trains. A quick sorry to jump in, I've gotta run to the restroom or I promised to say hi to the new guy, and I start moving while finishing the sentence. If they are mid-story, I touch my chest, say I want to hear the end but I need to handle something fast, and ask them to tell me the punchline later. The motion does most of the work. Last time I waited for a clean stop I ended up holding a plate so long I dropped hummus on the mayor.
