“The Torah obligation to thank Hashem for the state certainly pushes off the aveilut of the sefira, which is only a minhag.”
The word “certainly” is out of place in this sentence. It sounds like you are referring to listening to live music during sefira. While there are Rabbanim who posken that way, they are a minority. You can choose to follow that opinon if you like (and if that’s how your Rabbanim hold), but you can’t use the term “certainly” when referring to something that most of Gedolei Yisrael say is assur.
And the aveilus of sefira is halacha and not something to be taken lightly by saying “it’s just a minhag” which implies that it’s not halacha and doesn’t have to be kept.