I really do not know why the indefinite article "a" was absent from 1a. and 2b given that the precedent makes the uncountable noun countable:
1a. My friend paid me some money as remuneration for a job I did for him.
1b. My friend paid me some money as a remuneration for a job I did for him.
2a. John got a new car from his daddy as compensation for his damaged car.
2b. John got a new car from his daddy as a compensation for his damaged car.
They can remain uncountable; the difference between compensation and a compensation is onme of degree, I think; when the article is used, it sounds more like a gesture to compensate rather than an attempt to restitute fully.