I've not travelled from theStrip to Seville, but last year we travelled from MonteGordo to Seville with a Spanish Tour Operator. I'm sorry I can't remember their name, however they did advertise throughout the Algarve. It cost 20 euro, which was less than half the price First Choice were charging, and they were an excellent company.
If you haven't been to Seville it is well worth going, it is beautiful.

Many thanks.

I fly out on Tuesday morning and intend to go to both Seville and Lisbon.

I don't want to necessarily see the sights on route and would like a company who take a direct route.

I know I should probably take the train or a scheduled bus service, however, I'm also looking for the convenience of a local pick up.