This method is how the vape shops always teach new people but there are many other tricks you can use. Most cartos will come with the rubber caps on each end or "condoms". You can use the condom method which is you basically filling up the condom just under halfway and inserting the carto into it. The pressure of u pushing the carto into the condom will push the juice into the filler much faster. If this sounds confusing just youtube some videos. This will likely result in some juice wasting but not by much and it is MUCH faster! As for your going through too much juice problem it really depends on what mod you are using and basically the higher the power the faster the juice will vaporize. I don't see this really happening with the cig type you describe. Have you noticed any leaking? Sometimes these cheaper mods if they can even be called that are just not very good at regulating the batteries it may be burning way to hot. I would really recommend upgrading to at least an eGo.
The only leaking I've noticed is once in a while I get some juice on my lips... Is this normal?