Your description of how you were practicing sounds energetic enough, but with a lot of conceptualizing about the method based on presuppositions of what should happen. It's not surprising that rather than merge with the koan, you could exhaust yourself with it.
We all have our own obstructions like this and have to figure out how to work with practice. The teacher's job (among other things) is to oversee and advise. Impossible if we don't go to see the teacher, though.
If I were in your shoes and wanted to enter this dharma gate, I'd go back to my teacher and commit to practicing under that person's guidance even if it takes 25 years or a lifetime to break through the first koan. Nothing is lost by that. The "answer" to the koan isn't something you lack anyway. What is certain, however, is that your teacher's activities to directly point out to you that essential principle won't have much effect if you aren't there.
Aside from this, Torei has good advice:
If at this point your spirit and morale slacken, all the more rely on this vow/aspiration [to practice for the sake of saving beings]. If faith in the heart is shallow and weak, all the more rely on this vow/aspiration. If obstacles are many, all the more rely on this aspiration. If you are intelligent and clever, all the more rely on this aspiration. If you are stupid and dull, all the more rely on this aspiration. If your seeing into the true nature becomes fully clear, all the more rely on this aspiration. If your insight and function become fully free, all the more rely on this aspiration. Right from the beginning, from the first aspiration of the heart to the final end, there is no time when you do not rely on the strength of this vow/aspiration.
Reciting the Four Great Vows, directing them from the mouth outwards, and inwardly ever holding them in the heart, invoking them as a prayer day by day and continuously pondering them, then just like a wondrous scent or an old strange custom, or like fine mist that yet drenches one's clothes, or as the smell of incense pervades and clings, so the awareness of Buddhas and patriarchs will ripen of itself and, benefiting oneself and others, everything will be accomplished.
To state it concisely: by the power of the vow of Great Compassion all karmic obstacles disappear and all merit and virtue/strength are completed. No principle remains obscure, all ways are walked by it, no wisdom remains unattained, no virtue incomplete … The first requirement for trainees, therefore, is to let go of "I" and not to cling to their own advantage.