I'm a state and local tax professional specializing in multi-state sales and use taxes. I have a client using Shopify and I file their monthly sales tax returns from the Shopify sales report. I know exactly what your dilemma is as I have advised my client on how to setup the tax rates in Shopify for states like Virginia which is origin based for sellers within the state but changes to destination based when sales originate from outside the state to customer's destination inside the state.
Since Shopify cannot calculate the tax correctly in these situations (without putting an "unrealistic burden" on your business by telling you to add every zip code in the state to the tax rates ) then my approach has been to use a higher rate (not necessarily the highest) in the state which will result in some excess tax being collected which must be reported to the state by one method or another. The first and best method to use is to report the excess tax on a separate line item in the sales tax return when it's available. Unfortunately this is not the case with Virginia.
So then I called the state to ask how excess tax should be reported and they explained that a "separate " filing / report had to be mailed into the state. After discussing that option with my client and explaining the additional cost to them to have me make the separate filing I then recommended that the excess tax be reported to the local jurisdiction of "FIPS Unassign" (rate = 5.3%) by backing into the taxable sale figure (excess tax / rate)
The rate I recommended my client setup in Shopify was 6% (either by using a zip code having a 6% rate or using tax override) because the majority of their sales (73%) were actually made in those jurisdictions while 23% were made in 5.3% jurisdictions and 4% were in 7% jurisdiction.
Something to keep in mind when using the "grossing up taxable sales" method... Be sure to keep detailed documentation (work papers) that support the figures reported on the sales tax returns because under a sales tax audit you will need to explain why the actual taxable sales (from your sales report) were less than the taxable sales filed on the return. Hope that makes sense.
Hope you find this explanation helpful. If you'd like further assistance feel free to email me at firstname.lastname@example.org