Generally meditation is not really a jewish thing,
I realize you are not in NYC, but you probably need to come visit, The Carlbach Shul might have some meditation.
You might also like the services there as well. There is alot of singing and Cantorology there as well. You also might find some people like yourself (Age and profession) both men and women.
In Ultra-Orthodox shuls there isnt much singing anymore and even more modern shuls there is alot less of it as well. Nowadays when there is a rare cantor, you usually hear groans in the audience that prayers will take longer because there is a Cantor.