How can I properly vent a dryer whose ductwork comes up vertically from the ground?
You need to accomplish three things.
Weatherproof the duct

Make sure no soil is in contact with the duct
Seal the duct seams with foil tape and/or silicone caulk
Provide a drain path for rain and groundwater falling into the well, such as a pea-gravel basin or a French drain
Provide rain protection with some sort of cover or roof

Insulate the duct
You want as little exposure to cold air as possible to prevent heat from flowing out through the metal. Wrap the duct with foil-faced insulation sleeve.
Cap the duct with a louver
Your idea to use an elbow and a new vent louver is reasonable. You could possibly reduce the profile depth of the assembly by using a duct box and mounting the louver to that, rather than an elbow. Any dryer vent louver that fits the box or elbow should work.  The critical goals are to keep cold air from dropping in during winter, and to keep pests out.