If you removed the wood ,then two or three water changes of 40 to 50 percent should clear the water.
Water changes won't affect cycling to any negative degree, for the bacteria we are interested in cling to hard surfaces in the tank like filter material,rocks,gravel,glass,plant's.
I have next to no confidence with bacteria in a bottle product's and would, were it me,,be adding some type of food for bacteria in the way of fish food ,dead prawn,or liquid ammonia to help build biological filter /bacteria colony,, but some swear by these product's (can go to hell for this
Live plant's and lot's of them can also be of benefit while establishing the tank and could allow for a very few,,smal,, fish with additions every two week's or so without harming the fish.
Plant's will take up ammonia created by these small fish along with waste,fish foods, and tank can mature slowly but surely so long as not too many fish are added at once,,not too large of fish are added at once,and fishes are not fed too much food.
If you know someone who already has a mature,established aquarium running,you could maybe ask them to let you have some filter material from their tank and possibly a cup full of gravel, and place these in your tank and this too would help the bacteria colony get established assuming some food is present for bacteria to feed on as mentioned previously.
More than one way to achieve the result's desired
Agree with those above,tannin's staining the water may be unsightly to you or me ,but fishes could care less, and eventually the wood will stop leaching without any extra effort other than weekly water changes.