In practice what you do is pay the DIFFERENTIAL of taxes paid to the original state, and then keep your records of ONE TIME payment to all states.
Example:
7% sales tax paid to original state; new state @ 5% .... you owe NOTHING in sales taxes.
5% sales tax paid to original state; new state @ 7% .... you owe 2% to the 'new' state.
0% sales tax paid to original state; new state @ 7% .... you owe 7% to the 'new' state.
Caution: This does not include places that require ANNUAL personal property-type taxes (some/many counties of Virginia, etc.), where a 'yearly' tax of upwards of 5+% must be paid on 'assessed value', and depending on exactly the geographical location of the item during 'the first two weeks of January', etc. This is for boats/cars/trucks/aircraft, etc. etc. etc.