Multiple items in different shipping classes in order confuses shipping options

I own a brewery, and we are trying to get our site set up.
I have 3 shipping categories: Gift Cards, Gear and Glassware (which correspond to my product categories).
I have a single shipping zone, US, which has two shipping methods: Local pickup and Flat Rate. Flat Rate has no base cost, and only a single shipping class cost ($2 for Gift Cards; Gear and Glassware are N/A). Calculation type is Per class: Charge shipping for each shipping class individually.
Gift Cards are all marked as Tax status = None, Tax class = Zero rate.
Everything else is Tax status = Taxable, Tax class = Standard.
The reason for all this is that I don’t want to deal with taxes. Since gift cards are non-taxable, I have no problem shipping them anywhere (in the US). Everything else, however, I want to only be picked up in the taproom (because that then creates the tax nexus there, and I’m already submitting taxes for the taproom).
All this works fine if all of the items in the cart are within the same shipping class. If I only have gift cards in the cart, I get both options (Local Pickup for no additional cost, or Flat Rate at $2). If I only have non-gift card items (e.g. a T-shirts, glassware), I only get the option for Local Pickup. So far, so good.
However, if I have items in the cart in both shipping categories (say, a gift card and a T-shirt) then I get both shipping options available for selection: Local pickup for no additional cost or Flat rate for $2.
Obviously, in addition to the tax issue, T-shirts don’t fit in an envelope and will cost me MUCH more to ship!
How can I get this set up so that if there are both a gift card and a T-shirt that ONLY Local Pickup is an option?