Unless you love the go-nowhere bike (the trainer), 2-3 hours there at a time can easily destroy your motivation to even look at a bike. Suggest instead shorter but much more intense sessions in the trainer. With the allotted time you say you have for training, you'll have to make that time count with more intensity rather than riding at your expected pace. Lots [lots lots lots] of interval workouts. Make every minute count. Then as weather and time allow incorporate some longer "at pace" kinds of rides.
Definitely ride the Lama more, if that is going to be your bike of choice. You want to be most accustom and adapted to the bike you intend to ride. Just guessing (having not looked any of them up) that every bike you described rides differently and stresses the body in different ways..."Train the way you race" Also make sure the Lama is suited for the ride, averaging over 14mph for 14 hours...
Sounds like a great ride, best of luck.