What about having Four capture points on the lanes and moving the fifth to the center of the map?

Yes.

It couldn't be any longer than the bottom lane anyway.

I think modifications to the quest system would solve the bot lane problem issue you mention as well. (though in my experience going bot lane can be very action filled, it depends on the people in the game and the specific champions).

The fix would be that A) the quests will ONLY ever spawn on the bot points. and B) they have specific times ie 5 min, 10 min, 15 min that they pop. This will encourage a variety of play as there are a lot of different options, much like the baron spawning in SR. You can push for it, you can counter push while they are taking it, or you can try and defend it. This would bring a lot of focus onto bot lane during certain points in the game and would liven things up a bit.

Also, i do not agree with adjusting the layout of the map. i think many of the issues can be corrected through other things, and changing the map would be a very drastic, last resort in my opinion.

I did a huge thread about all the concerns you bring up, i mostly agree, one of the exceptions is that revive is good to have in the map, no, it should be eliminated in all ways shape , forms or thoughts.

The other thing about bot lane, is that it's the linchpin of the entire game.

If you can win bot lane, you force their team to react and come bot weakening them and preventing them from ever having equal numbers at top.