I might suggest Сейчас у меня свободного времени мало, так как я постоянно на работе. ("I have [too] little free time at present, since I'm constantly at my job.") You could change сейчас to теперь in order to emphasize that in the past, you didn't work such long hours. And you can say всё меньше и меньше to mean "increasingly less as time goes by" rather than simply "too little."
В последнее время and всё время are both correct as you've used them, but I thought they made the sentence sound repetitive.
And to me, вечно seems closer to "eternally" than "constantly" -- but you should ask a native Russian!