Other than doing singing more which is already on the itinerary.
you have to mean what you are singing. so, an interesting trick sometimes is to improvise the lyrics. it's like in conversation, when you have a conversation, you are improvising the words. that sounds normal and good, where as if you read a transcript instead, you are reading someone else's words from a different time and place, and it usually sounds fake and wrong. it would take some strong acting skills to actually convince yourself that those words are real at the time you are saying them. but that's really the only way to get the voice to sound any good. is if your brain thinks you mean what you are saying. so the best fast-track to this vocal state, might be to improvise the lyrics. could be worth looking into. if you get used to how that feels, this might help you conjure up a similar experience somehow, even when you have to be on script