Firstly, if your LED spec is 2.85 - 3.15 V at 1050 mA, the power is 3.3075 W. The maximum power may be only allowed for short durations, and the voltage will be a bit larger.
Can you share the LED specifications?
The LED will generate quite a lot of heat. The majority of the electrical power will end up as heat which has to be dissipated somehow. LEDs are a bit more efficient at lower powers, so it may be better to have more LEDs running at lower power, which will mean less overall power and heat to be dissipated.
An LLC converter is complicated, and while it may be slightly more efficient, it it probably much more difficult to design. I suggest that you have either a buck converter to reduce the voltage from the battery to the LED voltage, or you have two or more LEDs in series and have a boost converter to increase the voltage to the LEDs.
It's also worth considering a linear regulator. That will be far easier to design. If the LED voltage is 3 V, and you have a Li-Ion battery starting at 4.1 V and finishing at 3.4 V, the average voltage is 3.75 V, so the average efficiency will be 80%. I know that's not a really good efficiency, but a single 18650 battery will run the LED at 1 A for over 3 hours, and a really efficient converter would push that out to maybe 3 1/2 hours, so I don't quite see what you will usefully gain from a few percent in efficiency.
Also what is the reason for the high frequency requirement. The inductor will be physically smaller if the frequency is higher, but you will tend to get less efficiency.