Do you know how a VC would react to a company that has dozens of CAB members on the cap table? Could this create logistics/regulatory nightmare later?

You can create an Advisory SPV and put all your advisors on it. It would then be only one line item on your cap table.

You can also create a pool of shares (could be advisory share or something on those lines) from which you give them shares and since it's one of the option pool, investors should be fine with it.