KEEBLER:
You can get very strong on a trainer. Why don't you do some isolated leg training (ILT)??? It will make your legs stronger and improve many other areas of your cycling.
Some coaches don't believe in it, others do!!! Coaches and riders at the world-class level believe in it, so give it a shot and see for yourself if it is true or not.
You can do your ILT with the front wheel elevated to simulate climbing quite effectively. ILT will fatigue your legs quite rapidly, forcing additional muscle fiber recruitment. This will lead to hypertrophy (growth) and enhanced neuromuscular fitness, all of which make you stronger.
If you study the bodies of time-trial specialists, you will often find they have larger butts and thighs than "normal" road riders. This is extra muscle they have packed on from pushing big gears while seated.
More muscle means more strength, which leads to increased power output. Power= work/time, or in the cyling world, pedal force/time. Stronger mucles produce more pedal force, and last longer before fatiguing.
Put your bike in a 53x11 on the road and ride at 10 mph. That doesn't require much power at all, yet it will feel much harder that riding in a 39x21 at the same speed. The main difference between the two gears is pedal force. Stronger muscles generate higher pedal forces easier than weaker ones.
Find out for yourself what the truth is!!!
Good luck!!!