Noelia, of course, I can’t give you legal advice on this but here are a few personal thoughts of mine.
I wouldn’t give up just yet. I think you should pursue this a little more so that you can understand better the different options available to you and their likelihoods of success. (btw. Any trademark application is never guaranteed USPTO approval and all TM apps run the risk of big expenses – you just have to judge the likelihood of success and potential cost before pursuing it.)
Option 2 for example, a Design Mark might do the job. I don’t know why you say that it involves significantly increases costs. I have both a Work Mark and a Design Mark and they both cost me the same (but I did not use a lawyer so I avoided their costs).
Amazon Brand Registry will accept ‘Design Mark’ Trademarks as long as the ‘literal element’, i.e. the letter and numbers in the logo, match your Brand Name EXACTLY. If you are still using #80 as your logo, you would have to remove the “E 2020”. Also the #80 logo makes MOM CODE look like one word MOMCODE. You’d need to alter that too probably.
Or, an alternative idea is for you to register a Design Mark for MOMCODE, i.e. no space, and change your Brand name to one word MOMCODE. This would reduce the chance of other ‘Mom’ or ‘code’ trademarks challenging your Mark. Especially as it is a Design Mark, I think it is probably more difficult for owners of Work Marks to challenge your Mark.
In my opinion, the single word MOMCODE works just as well as a Brand Name.
Anyway, they are a couple ideas that hopefully help you generate other ideas too.