I move the dryer forward (disconnecting vent pipe and electric cord while doing so), and use the shop vac to clean behind and under the dryer and in the duct bends behind the dryer and up in the exhaust tube from the lint screen, then tilt the dryer up so I can reach in the open bottom and vacumn all that, then carefully (so as not to puncture or tear loose the exhaust duct) run the shop vac hose as far in as I can into the in-floor exhauset duct.
Then I run a loose swap like a swifter brush on a string through the vent pipe/hose - a swab that is close to but slightly less than the vent hose size, so it does not jam up in it - this knocks the adhering lint off the duct walls and bottom.
Then I duct-tape a piece of ABS or PVC pipe that is similar sized to your vacuum hose to the flex hose on your shop vac, so you can reach further in the vent pipe (assuming it is a straight run to the dryer). If not a straight run, then you need a long enough vacumn hose - you can duct tape on a second vac hose, or a piece of workshop central vac flex tubing that you can buy at your hardware store. That way I can reach in from outside for 10 feet with one pipe length, and vacumn out all the lint the swab knocked loose. If the vent is really linted up , vacumn BEFORE swabbing so the swab does not pile up a big pile and get stuck, then again after swabbing.
I just vacumn only every year, then swab about every 10 years and it stays quite clean in between, with a 20 foot duct run to the outside louvers.
There is a LOT of discussion regarding whether round metal or plastic ducting or corrugated flex tubing is best for dryers, although in some areas the building code mandates one or the other. For my money, a straight pipe like ABS or round ducting seems to build up a lint coating MUCH faster - I changed over to flex tubing and the resulting flow turbulence really cut down accumulations.