Why even bother with the landfills? There are massive garbage patches floating around in the oceans, the vast majority of which are plastics. If you can get a big enough tanker and implement this system on it, you could probably cut the amount of fuel needed even further - the tanker goes into a garbage patch, melts all the plastic down, keeps the oil, and uses some of it to get back to land. It would probably be more effective than loading fleets of trucks.
You are vastly overestimating the density of these patches, probably due to media sensationalism. For example, the "Great Pacific Garbage Patch" has a density of 4 particles per cubic meter of water. These particles are quite small, even microscopic. I know the news stories make it sound like it is just this mass of garbage floating around but that's just not how it is. From the Wikipedia article linked above:
"and the relatively low density of the plastic debris at, in one scientific study, 5.1 kilograms of plastic per square kilometer of ocean area"
I doubt it would be cost-effective to process a square kilometer of seawater to get that paltry amount of plastic, even assuming you could recover 100% of it.