Some travel agencys might try to play you and have you book hotel as well...of course they make more money that way.
Many of Europe's big airports have direct flights to Bangkok so should be no problem at all getting there, getting a flight to Phuket from Bangkok you can do when you get there.
Some even fly to Kuala Lumpur, where you can fly directly to Phuket...or from Singapore for that matter.
The options are in fact endless and it should be no problem flying to LOS without getting suckered by a travel agency.
Just to mention a few options, direct flight to BKK from Amsterdam, London and Frankfurt. Suspect loads of other places as well without having checked
Then it all comes down to price and availability.
If you cannot 'loose' the hotel booked I suggest you book a cheap hotel upon arrival, it will at least be far cheaper then a 3k joiner fee.
Next trip, unless you have a very good travel agent that know and apreciate you as a customer, try getting it straight from the source. Book with the airline itself.