Contact the City Building Code people. They can tell you what your address is zoned for and can get you forms for filing for a variance or conditional use permit. I don't honestly know where a FFL would fit into the Codes or Tacoma's local ordinances. This might might sound naive but nobody should know more about difficult zoning than the marijuana dispensary people and their lawyers. Make a few calls and ask.
It would be a good idea to check the local zoning ordinances (the Tacoma Municipal Code is online) so that you do not invest in your business and realize that you cannot operate it.
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyze this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here
To determine if you can operate your business from any address, start first with your City's Municipal Code. If you are in an unincorporate area of the County, check with the County Code. Most codes are available online and you can find them with a simple online search.
I recommend, in all cases, that as a business owner you make it one of your most important tasks to meet your local officials and law enforcement personnel and maintain an excellent working relationship with them at all times. This will benefit you tremendously now and into the future. This is particularly so if you are selling firearms. Good luck.