Take more, switch brands & take the other 2 items

Three teaspoons is a pretty small dose - more of a maintenance or preventive dose than a therapeutic dose. If it were me I would take ounces of CS at a time - perhaps 8 ounces the first few days (2 ounces four times daily) and then reduce to a couple of ounces until the Lyme is conquered and perhaps switch off to Utopia Silver's Advanced Colloidal Silver (a true colloidal silver and not mostly ionic like Argentyn) or Purest Colloids Mesosilver (likewiise a true colloidal silver). Don't worry about takiing too much CS - it is safe to take a lot of it over a short period of time. I have taken up to 8 ounces a day several times and take ounces of it whenever the need arises.

I am not familiar with Banderol but cat's claw is really good stuff and I don't see any reason not to use both of them, particularly if they are recommended by someone trusted and others have had success with them.