Power factor correction doesn't apply to DC. Power factor is the phase relationship between the voltage and current waveforms when driving a reactive load with AC current. When the current waveform leads of lags the voltage waveform, the apparent power that you would calculate with Volts*Amps is higher than the true power being consumed. What you are describing is a boost converter, a DC-DC converter in which the output voltage is higher than the input voltage.

There are few reasons to use a linear regulator anymore for anything more than a few tens of milliamps. This is particularly true in battery applications where every bit of juice counts. The buck converter modules I've been using can be had for less than 3 bucks each and are super easy to use. Connect power in, connect the load, and there's a trimpot on the board that you can dial in the output voltage.

IIRC the monitor in a SE series Mac draws around 1.2A from a 12V supply. There is no regulation in the monitor itself so picture size will vary noticeably with supply voltage, a regulated supply is needed.