Thanks Eric @eb801!
You cannot buy liquefied styrene, you just have to make it at home very easily: I cut small pieces if styrene with my plier, put them in a small jar, pour MEK (methyl ethyl ketone), which dissolves styrene very aggressively, close the jar and let it stay for half a day or more; a uniform liquefied styrene will be produced.
You can vary the thickness by adding more styrene or more MEK). You can apply it with a toothpick or a needle or use a jar with a brush attached to the cap, it is really up to your preference. If you close the jar tightly, it remains as is, ready to be used again. If it thickens in the jar, just add some MEK, leave, and after some hours it's ready again!
You can even make two jars of liquefied styrene: a more thick for bigger gaps and a thinner one.
If you are cautious about using MEK, you can alternatively use the thinnest liquid glue for styrene you can find: it will do as good a job as MEK.
A note: When using it, put only the required amount at the concerned area, as too much will dissolve the surrounding area and may cause sink mark(s); just put a small amount to adequately fill the gap, leave it to cure, sand and voila! Should some small gap remain, repeat the process, or use normal filler!
Once you get used to it, you might find it useful at some intricate filling cases.
You may even implement Allan's @kalamazoo idea above: it's simply an amazing idea and I will for sure use this process as well!
Here's a nice explanation video on liquefied styrene:
Cheers!