Would this make any difference if the closest Eastern Rite Catholic Church is 500 miles away?
Not sure who you're asking about, but the closest Byzantine Rite church to you is more like 100 miles away. :-)
You can of course add a mention of the distance to the paperwork for a formal change of rite.
Keep in mind that there's probably no need for a juridical change of rite unless the person is interested in pursuing ordination. I think the other sacraments requiring jurisdiction (confession, for example) can be celebrated with a priest of another rite, if a Byzantine Rite priest is not readily available.