I would guess that "time is essential in this project" would sound logical and appropriate to your situation.
Note that the word essential is directly derived from the word essence; "of the essence" is one way of adjectivizing essence, and essential is just another way of doing so.
We do similar things with many words. A couple examples:
"Talk about something of substance" vs. "talk about something substantial".
"A statement of fact" vs. "A factual statement".
"I did it by accident" vs. "I did it accidentally" (in this case we are adverbializing).
It so happens that, nowadays, "of the essence" is rarely used, while "essential" is common. "Time is of the essence" is one of the few phrases that retains this construction, and so it sounds odd, but etymologically and structurally, it is straightforward.