Well, it seems that the low intensity portion of your training has been left out. There is definitely a need to base train, so read these articles for some insight.Why Go Low?Periodization in Strength TrainingOff-Season Training Analysis
One thing that you said that concerns me a little is
I find that I fatigue very quickly, not just lung capacity, but also general strength, the bike begins to control me instead of me controlling the bike. Hopefully all the strength training I have been doing will assist in that.
Max strength training will only address this problem indirectly. Hopefully your trainer will start transitioning to a period of endurance strength training. This article addresses
a lot of the questions you are asking. Pay particular attention to phases of strength training that are talked about in the article (Anatomical Adaptation, Muscular Transition, Maximum Strength, and Power Endurance).