Thanks for the help everyone. As of today, it looks like we will burn miles (I have plenty to spare in a non-OW carrier.) Most of the LCCs or charter airlines that I contacted wouldn't sell a one way ticket.
Originally Posted by DP-UK
I'd either burn current miles to get to CAI or use a one-way LCC.
If getting cheap return from CAI is a problem, you could always book another one-way LCC flight when you arrive back in Europe in April 06, or use some of the miles from the ONE.