I'll second the suggestion to just use one of the $99 "10 gun" or $179 "18 gun" steel gun lockers. Neither will hold the advertised 10 or 18 rifles, but they will hold a lot of ammo cans or boxes. With a drill, a saw, some wood and some screws, you can add shelves where you need them and make them much better organized for ammo storage.
I'm also a fan of the GI ammo can. As noted above you can add a long shackle padlock but they don't always allow a tight seal.
You can tack weld a u on the front of the box (cut link of chain, etc) where it will extend through the slot on the latch and allow you to install a small pad lock. If you don't have access to welder, you can install u-bolts, but you'll want to use washers on both sides with silicone adhesive in between to seal the holes and keep the can air tight. I use small combination locks to avoid what would otherwise be a key nightmare. It doesn't have to be theft proof, it just has to be kid proof
It's also really easy to designate a single closet in the house for ammo storage and just install a knob with a lock on it.
If you've got a spare bedroom with a large enough closet with a door, put the gun safe(s) in it, and the store the ammo in it as well. If you then set it up as a play room or put a kids bed and some toys in the room, it will get very low priority from thieves who primarily concentrate their efforts on the living areas and the master bedroom - since that is where the valuable stuff is kept. A closet in a playroom or young child's bedroom probably won't even be entered at all if there is some time pressure involved.
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As an aside, I'll mention that the vast majority of "fire proof" gun safes really are not. They won't prevent the guns inside from getting charred in a common house fire where the temps will be 1200-1800 degrees F at their peak and will take hours to cool in the remains of a fully involved house fire. So if you want fire protection - something along the lines of the 4-6 hour protection that is really required - come prepared to write a big check.
However, the far larger threat is theft, and theft is easier to prevent, provided you are properly alarmed and the thieves consequently have limited time to find and then open the safe. The second most likely threat is flood, and fire is a distant third.
In terms of fires, the most likely cause of a fire is cooking and kitchen related activities which are about 3 times more common than the number 2 cause - electrical fires. So rather than spending money on an expensive fire safe, focus on prevention, buy some fire extinguishers for the kitchen and do good preventative efforts for electrical fires - unplug chargers that are not in use, use care in using electrical heaters, and get AC and heating units inspected annually.
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The inadequate fire protection rating of most gun safes is relevant of course because if you've got ammo cooking off in the house, unless there is still someone trapped/missing in the house, fire fighters are not going to go inside until the ammo starts cooking off. It doesn't matter that the rounds are probably not leaving the ammo can or steel cabinet they are in, and if they are, are probably not carrying enough injury to inflict a wound.