An English /d/ is normally produced with the tongue tip at the alveolar ridge. Your attempting a dental /d/ before /th/ might not be a good idea, because, as you say, you still have to slide it between your teeth between the /d/ and /th/.
For "Would the ..." I find I make only one tongue position. The tongue tip goes between the teeth in anticipation of the /th/ while simultaneously the part of tongue behind the tip touches the alveolar ridge momentarily to make a proper alveolar /d/. This is also the case in words like "width, breadth ..."
(It might not work for you!)

Student or Learner
Bookmarks