Video taping may not be the preferred way to go about it, but there is something to be said for reflection. While you are unlikely to get better without practice, merely sinking time into conversation won't necessarily help, and may harm you. Without analyzing your attempts, even if it's only a brief list of what went well and what didn't, you may be practicing and learning bad habits. 100 ungraded math problems doesn't make you better at math, and 100 uncoached squats may injure you.

Take a few moments after conversations to assess at least what went well and what didn't. If you have access to an honest friend, you can do even better. Converse with a third party (your friend can participate or merely be near enough to observe) and run a sort of post-conversation analysis later. Treat it like any other skill you're serious about learning. I've seen this help more than one struggling introvert.