Removing invasives is an inevitable part of converting a landscape to a rich habitat for wildlife, so getting really efficient at it makes good sense. Here's a somewhat obscure tip: Get to know the stems of your plants.
Being able to assess at a glance which stems are the good guys and which are the bad allows you to grab a handful of stems or cut a stem near the base of bad guys and, with any luck, remove entire plants. This is way faster than pulling out individual portions of an invasive plant from above. Part of the "getting to know your stems" process is getting a feel for how the stems feel when removing them. For example, the invasive stiltgrass pulls out easily without disturbing the soil, so if you feel any resistance when pulling out a handful of stiltgrass stems, you know another plant is in that handful--one that you may or may not want to remove.