If the screen takes 48W (4A at 12V), you won't be able to power it from a battery that delivers max. 24W (1.5A at 16V), no matter what kind of regulator you are using. You will either have to change to a bigger battery pack or find a less power hungry screen. What kind of screen is that anyway? 48W is rather excessive for any kind of screen I could imagine running on battery power.
A few additional points to keep in mind:
- Don't connect regulators in parallel; no two will have precisely the same output level, which means that only one of them will end up driving the load, with the other possibly even (depending on the design of the regulator in question) just providing an additional load.
- Switch mode regulators capable of handling >4A certainly exist. I don't know what is out there of ready-made modules, but LM2678 to name one, is a switch mode controller capable of handling 5A. Note that this kind of controller requires external components to make a complete regulator circuit (see datasheet).
- For relatively low voltage drops, like 16V to 12V, linear regulators may be worth looking at again; 16V to 12V would mean 75% power efficiency; bad by switch-mode standards but not outrageous.
- On the other hand, with high currents, each percent of lost efficiency means considerable power waste in absolute terms.
- Remember that all power "lost" will wind up as waste heat, meaning that inefficient and/or high power circuits will require a heatsink, in extreme cases a quite large one. Allowing silicon components to reach tea-making temperatures is not recommended
Best regards, Kári.