stewardship generally isn’t hereditary in asoiaf and many stewards seem to be glorified servants (or viewed that way). so why did the gardeners “reward” the tyrells (for what seems to be awesome service) by making their family the stewards permanently? would an ambitious and clever family like theirs have had better prospects in the long run if they hadn’t been made stewards or was that the best they could’ve hoped for?

This strikes me as a bit of fanon. Stewards have last names, it’s considered an honorable enough title to have Lord Stewards of the Watch and High Stewards of the Vale, etc. Stewards are very close to lords and kings – Eddard says to give his letter to Stannis only and “not his steward, nor the captain of his guard, nor his lady wife,” which shows you how close. 

Remember, in a feudal society, proximity to the king is power. So in our world, noblemen competed to get the position of being the Groom of the Stool despite the fact that most people today would consider that extremely degrading labor.