How much should this shower remodel cost and is there a way to fix my issue without remodeling?

Picture attached to show the shower that needs remodeling, but I just moved into this house and have realized that there is a slow leak somewhere in the floor of the shower. Overtime it has stained the subfloor below in the unfinished basement and now that we are in the house we have noticed a very tiny drip Into the basement below. I have a handyman that has given me a bid to fix the shower but he says the only way to do it is to rip out the entire shower because he believes that the membrane underneath the tile floor is not connected correctly to the drain and thus it all has to come out to put in a new membrane and go up the side walls. We have no desire to change any of the tile in the bathroom so it really sucks to have to do a complete remodel just to put back everything the way it already is. He is quoting about $7500 for demolition and labor that would include the material materials except for the tile itself which will cost another roughly $1500. So two questions… Is $7500 in labor to demolish this and put it back together correctly reasonable? I was thinking substantially less. And then number two and even more importantly, is there a way to possibly fix this issue and/or install a new membrane without taking the entire shower apart all the way to the ceiling? Should somebody be able to just go about a foot up on the sides and adequately match the new tile install or is that way too hard?

Picture attached to show the shower that needs remodeling, but I just moved into this house and have realized that there is a slow leak somewhere in the floor of the shower. Overtime it has stained the subfloor below in the unfinished basement and now that we are in the house we have noticed a very tiny drip Into the basement below. I have a handyman that has given me a bid to fix the shower but he says the only way to do it is to rip out the entire shower because he believes that the membrane underneath the tile floor is not connected correctly to the drain and thus it all has to come out to put in a new membrane and go up the side walls. We have no desire to change any of the tile in the bathroom so it really sucks to have to do a complete remodel just to put back everything the way it already is. He is quoting about $7500 for demolition and labor that would include the material materials except for the tile itself which will cost another roughly $1500. So two questions… Is $7500 in labor to demolish this and put it back together correctly reasonable? I was thinking substantially less. And then number two and even more importantly, is there a way to possibly fix this issue and/or install a new membrane without taking the entire shower apart all the way to the ceiling? Should somebody be able to just go about a foot up on the sides and adequately match the new tile install or is that way too hard?