If the webpage were designed correctly you could just use Chrome or Firefox's zoom out feature and then take a screenshot within the browser which would record all the pixels rendered not just the ones getting to the screen. Unfortunately its not going to help you even if you used some other tool without editing the page itself.
You can test that this is not the fault of OSM by going here: http://www.openstreetmap.org/ and using Ctrl+- and seeing that more field of view is rendered when zooming out. And when looking at Leaflet here: http://leafletjs.com/examples/mobile/example.html it also behaves this way.
Therefor you will need to hack it to do what you want. Use your web browsers style editor and add the following:
html, body {
height: 100%;
}
#main_map {
height: 100vw;
width: 64.64vw;
}
then tick the zoom in and out on the leaflet UI then you can use the browsers zoom features.
xrandr
will create you a virtual desktop of any size that your memory allows. I often use this to create a screen-shot of an image that is bigger than my physical screen size, without the loss of detail that comes with scaling.