Pepper on a stick

Hello Rabbi. I am Sephardic and I often pray with Ashkenazim (in my sins) and there are days when they don't say Tachanun for reasons that are unacceptable from a Sephardic perspective. I don't change from the local custom and don't say it with them.
There is no problem with the first part of the supplication. The question begins with the accompanying parts. As is known, 'Lemonatzech' and 'Tefila LeDavid' among the Sephardim depend on the supplication – if there is no supplication, there is no them either. Among the Ashkenazim, they are not always related and they may be said even when they are not said.
The question is, in a situation where they don't say Tachanun for an 'Ashkenazi' reason but do say the Tosafot, do I need to say the Tosafot or not? The sides are as follows:
The Tosafots should not be said because I do not say Tahanun and for me the Tosafots are related to Tahanun.
Or go this way:
The Tosafot must be said because in my opinion the entire supplication should have been said, and just because I am in a congregation that does not say it, I do not say it along with them, and they do say the Tosafot, and it is enough for it to be considered a sin.
And if you say to say it anyway, and if it doesn't help, it won't hurt, then according to Kabbalah, everything that adds detracts from the order of the worlds.
And perhaps it could be said that what they said according to Kabbalah, that everything that adds to something detracts, was specifically in matters that are not part of the order of prayer at all, but in matters whose place and belonging in prayer are disputed or in customs, this ruling does not apply.
I don't think bath salts like these are the Rabbi's cup of tea, but maybe the Rabbi (or one of the surfers) can throw out some interesting ideas.
Thank you very much.