What factors or parameters control 'presence'?

EQ should be your next stop. Try losing some top end and see if it helps.

You can also experiment with a little delay... very short times to start with though, otherwise it becomes too overt.

"Presence" is usually an EQ term, referring to the band between about 4KHz to 6KHz, where vocal consonants (including "essiness") and plucked string attacks are most prominent. For spoken word, it's the band most responsible for comprehension of what's being said. For electric guitars, it's where the "bite" lives.

Reverb, on the other hand, is used to position a sound's imaginary position front to back. In the real world, we hear more reverb from sounds that are further away, less reverb from sounds up close. Consequently, our brains associate reverb with distance, so you can make parts sound further back in the mix with reverb.

I you're trying to get vocals (or any lead part) to move up front in the mix, use less reverb, not more.

If you want a thick, lush effect on a lead vocal but reverb makes it too mushy, try using short delays instead of reverb. Using two different delays for left and right channels can make a rock vocal sound really big.