Uhm, at the moment i have nothing as switching / boost at home, that can reach this current, but if for you is enough also a linear, can arrange a paralleled unit with 3 x LM1117 (same producion lot) in SOT223, decoupled with 0,1 ohm resistors at the inputs, with a 0,96 ohm (or better said, a combination with that value) as current sensor resistor ..... the 3 IC can hold 800mA each, so for the current must be enough (can also be enough 2, but are close to the limit, and i always prefer stay abundant)
the LM1117 have a declared dropout of 1.2V, so you need at least 3.5V, but is better use at least 4V ..... a 3,7V LI-ION may be enough, but when it discharge and go under 3.5, it become too low ..... a 4,5V supply can be good, just a bit more dissipation, but using AAA batteries, are you sure that they can give you 1.3A ?
As alternative, i'm waiting some samples from on-semi, that they claim can be used for make switching boost/buck converters until 1,5A, but i don't know how much time they take for arrive here, and then i also need to do some experiments on them, before build something useful (is a new product, and i never got them before, so until i don't have them in my hands for test, i know nothing about them, except that what they printed on the datasheets), so no ideas at all, about the time that this may take .....