False Tooth for Lower First Molar? Is it possible?

Missing teeth ALWAYS need to be replaced. An un-replaced tooth will cause the opposing and adjacent teeth to move and shift, which could ultimately result in their loss too. I think you are wise to not want to cut down perfectly good teeth. A good option for you since you do not want a dental implant (which really is the best solution), would be a removable partial denture. A permanent partial has a chrome framework that is very strong, unlike an all acrylic flipper. I am perplexed as to why this option has not been presented to you? Good Luck!