To be honest, for a bunny that's just a year old, taking out the molars might be the option that costs less in the long run and has less suffering. It's a serious procedure, but considering that once he recovers, which will be much quicker than for an older bun, he won't need any more tooth work, that would be a great benefit.
Usually we see this kind of tooth thing come about at age 4+, unless they've got a "heavy genetic load" of bad teeth. For instance, if you got him at a pet shop, he may have been poorly bred. Many (not all) of the bunnies sold at pet stores are bred by non-professional breeders--what some would call backyard breeders. A more professional breeder will choose not to breed bunnies that have bad teeth or whose offspring have bad teeth because they don't want bad teeth genetics in their lines. People who breed to sell, not to show bunnies, often do not choose to remove bunnies with bad teeth from their breeding stock. For this reason, speaking in broad generalities here, pet store bunnies of the smooshed face bunnies (lops and dwarves) often have bad teeth. Of course there are some pet stores that sell bunnies that were bred by professionals, and some professionals are not good about removing bad teeth genes from their lines, and some very well-bred bunnies get tooth problems later in life, and some pet store bunnies were bred by responsible people that do keep the bad teeth out of the lines, etc. I'm just painting this in broad strokes. I hope you understand what I mean. A lot of bunnies in shelters too were once pet store bunnies that got surrendered to the shelter when they were no longer wanted.
What I'm trying to say is that it is rare for a bunny to have tooth problems that require trims monthly or every 6 weeks at age 1, and it probably will not go away. He is young and will heal faster from tooth extraction surgery than an older bunny. The cost over time of getting repeated tooth trims too could amount to more than getting the molars all extracted right now as well.
