I chose wifi over bluetooth because of the lower latency and ability to possibly stream video in the future.
Describe that technology (WiFi over Bluetooth) please because that's not a common term. BTW streaming video to an Arduino doesn't make sense (missing resources on the Arduino side, RAM and processing power).
Is there any way I could get 300m+ without any hardware changes to the phone?
With line of sight and a directed antenna you might get that by WiFi.
You should start by telling us what you want to achieve. Maybe the community has some alternative technologies for you.