Our house is semi-baby proofed. When we moved in, most of the cabinets had the safety locks on them, so we left them attached. It also had the cushion around the brick fireplace edge. So we left it. Most of the main floor (ranch) is hardwood floors/ceramic, so we've had some bumps and bruises on Jacob. I do understand that your situation is more specialized with your sons tantrums.
I've found that we don't really need to do much more at this point. We have glass shelves for our TV equipment that he's not allowed to touch. We have a gate by the kitchen but we have two German Shepherds that would lick our son to death! Other than that, we let Jacob in all of the rooms - with supervision. He likes to spin the office chair, pull all my books off my bookshelf, look out the windows in his room, play on the "big bed" (our room)...etc.
Maybe you can try to let your son have access to the bathroom so he isn't so preoccupied with being allowed in an "off-limit" room and feels comfortable in there. The same for your daughter as her potty-time will come soon, too! I'm not saying the bathroom is a playroom and I know there are major dangers in there, but kids (and animals) seem to want things that we don't let them have! Lol. SO, maybe just being in the off-limit bathroom is enough for your little guy. Take that excitement away and maybe it will help. As long as you put the cabinet locks on and supervise any activity in the bathroom, I don't see much of an issue.