Just to warn you that the filter start will probably not do much. The only ones known to help sometimes are Dr Tim's One & Only (but that's hard to get in the UK) and Tetra Safe Start, and they only work if they've been handled properly. All the others contain the wrong species of nitrite eaters.
Are you adding ammonia as well?
Your sponges will be the main home for the bacteria once they've grown. There will also be some in the carbon sponge. You can leave that there permanently though it will stop adsorbing things fairly quickly as it gets full. You can replace the carbon sponge, though you will also remove the bacteria on the old one, or leave it there even though it's stopped adsorbing things, or replace it with plain sponge. If you want to get rid of tanins on a long term basis, it will need replacing frequently.
If you take the wood out now and pour very hot water over it a few times, leaving it to soak between, that will get rid of a lot of the tanins. Then if you put it back shortly before the cycle finishes, it will have time to affect the water before you get fish. It won't change things that much.
As a side issue for anyone who is interested, regarding bacterial starters -
When these products first came on the market, it was thought that the ammonia eaters were Nitrosomonas species and the nitrite eaters were Nitrobacter species. Then Dr Tim Hovanec, working for Marineland, did some research into these bacteria. He found that the ammonia eaters were indeed Nitrosomonas, but he discovered that in aquariums the nitrite eaters were not Nitrobacter but Nitrospira species. Marineland and Dr Hovanec patented Nitrospira (or formulations containing Nitrospira) which prevented other companies using the correct nitrite eating bacteria in their products.
Dr Hovanec left Marineland and set up his own company - because he is named on the patent he can use the correct bacteria in Dr Tim's One & Only. Marineland was taken over by Tetra, so Tetra can use the correct species in Safe Start. No other company is allowed by patent law to use Nitrospira. They can use the correct ammonia eating bacteria, so that stage of the cycle can be speeded up by using one of the other brands, but with the wrong species of nitrite eaters, the second stage is not speeded up at all.