There are not too many Sunday Masses in our area that are reverent. Our “daily” Masses are pretty good, though. They (6:15 a.m.) are Novus Ordo, and there are no Eucharistic Ministers (or any altar servers). The only strong distraction is the Sign of Peace. However, if there was a daily TLM in the area, we would switch and go there. The two different forms of the Mass (after one has attended for awhile) seem almost like two different faiths completely (in our opinion). How many TLMs have you been to?
Allow me to shove my nose in here for a few minutes. I live in the epicenter of reverent NO Masses: Greenville SC. Within screaming distance we have Fr. Dwight Longenecker at Our Lady of the Rosary, Fr. Jay Scott Newman at St. Mary's and Fr. Christopher Smith at Prince of Peace. Those three priests are known the world round for liturgy, theology and dedication to Our Lord. They're all three converts for that matter.
With all the rich options available to my family we choose the simple sung EF Mass at Prince of Peace because it's the only time and place we can be at Mass without being jerked back and forth between the sublimity of prayer and the banality of the new ritual.
I understand the NO has had a major revamp in language recently but that's not enough to fundamentally change the horizontal nature that's built into the rite itself. There's only so much window dressing you can put on the NO before it starts to look like a parody of the EF and therein (I believe) lies the problem: At its core the new ritual is not supposed to be "reverent". It's supposed to be exactly like it is in most places.
That's my 3 cents anyways.