First, I would encourage you to review SecureIt's website regarding the failures of chinesium safes, as that's the most likely cause of the odors:
https://www.secureitgunstorage.com/gun-safe-corrosion/https://www.secureitgunstorage.com/how-the-gun-safe-industry-lost-touch/https://www.secureitgunstorage.com/do-you-need-a-fire-rated-gun-safe/And I'm not affiliated in ANY way w/ sole exception of aspiration owner of their products (meaning, don't yet own but intend to upgrade in order to).
I do think it's prudent to develop a fire resistant envelope around your Secureit cabinets (build them into fire-rated drywall double or triple layer, maybe plus up rear/side security, consider replacing wooden studs w/ metal, etc) and then also use fire resistant containers w/in them for valuables if you don't have a fire-rate actual safe. Also look at locating fireball extinguisher(s) nearby -- goal is to buy time in event of fire before fire department w/ water tankers arrive...
Re: conventional safes, I think Brownings or perhaps the more premium Liberties (avoid their base models) are about the cheapest I'd go (but not devoid of issues you're referencing), and for classic safes, I'm likely going Pendleton as they're similar in a lot of ways to SecureIt (metal interiors, etc.), and likely only heirloom guns in that w/ other valuables/heirlooms and critical documents -- or if on more of a budget I'd look at Ft Knox w/ various upgrades or Amsec (haven't priced/featured these two recently, but both for Pendleton-like features cost quite a bit more for their true safes vs base "residential security containers")...
DampRid condensed water vapor is caustic (acidic/alkaline -- one or the other) IIRC and not good for metal, fabric, etc., if spilled, so just be aware. Citrus Magic Odor eliminators do work to absorb odors, but yes, ozone machines eliminate odors (can be had relatively cheap on amazon), but I would get all of my firearms out of the vicinity first as it's an oxidizer -- you also don't want to breathe it in. and baking soda and coffee grounds and sometimes vinegar in a bowl also work -- wouldn't use vinegar w/ my guns in the safe though.
In a gun safe, you definitely want to eliminate the cause of the odor, not just the smell. Definitely ensure you have humidity controlled and consider putting a small dehumidifier inside if new to remove as much moisture as possible from drywall lining your safe before worrying about maintenance solutions like DampRid.
Good luck! Please let us know what works for you.