B”h doing well
In your situation as it is a private shul the Shliach is justified no worries for any curse etc…chas vshalom
The passuk says regarding the Cohen “vikidashto”
[1] and one should sanctify him (as he brings the korbanos/ offerings to hashem), the rabbis in the Talmud deduced from this verse that in every ritual the Cohen should come first, in a gathering he should talk first, at a meal he makes the bracha first, when it comes to distribute or divide something the Cohen takes or chooses first ,and so too one is not allowed to use a Cohen out. and likewise, he is to get the first Aliyah at the torah.
[2]
These obligations also exist today although we don’t have physical korbanot yet the Cohen remains in his holiness.
Can the Cohen forgo on this mitzvah?
Some halchic authorities hold he can as the “chehuna” is his and he is allowed to forgo on it while others hold that he is only allowed to forgo on it if he has a benefit from doing so as a reward payment etc.
The alter rebbe seemingly rules that the Cohen is allowed to forgo on these things, and although some halachic authorities hold that regarding the first Aliyah the Cohen cannot forego (in order that fights should not ensue, as each person will say why did the Cohen let him first but not me).
[3] yet the alter rebbe holds that this allowance also includes the first Aliyah , as if he wishes to he can give over his Aliyah to a yisroel as he is allowed to forgo on his kavod / honor if he wishes to (as to fulfil one wish / desire that is his true kavod honor).
[4]
If the Cohen cannot go up to the torah we give his Aliyah to a yisroel example if it is a fast day and he is not fasting or if the Cohen is in the middle of shmoneh esreh, if the cohen is in the middle of birchos krias shema it is a discussion amongst halachic authorities if he should be called up to the torah in practice when there is no other Cohen and the custom in Ashkenazi countries is to call him up.
[5] In a situation where the Cohen is not being called up, being that not everyone knows why it is best that he actually leaves the shul (so people shouldn’t think there is a problem with his lineage).
[6] Yet if he doesn’t leave the shul it is ok.
Poskim discus a situation where the community had a custom (at certain times like Shabbos Berishis) that they sold the first Aliyah and didn’t give the Cohen poskim write that they are intitled to continue their custom as it was initiated in the honor of the Torah and all though the Cohen objects we don’t heed his objection.
[7] Poskim explain that the reason that the initial minhag was done with the agreement of the Cohanim (and the whole community), yet in a situation where they want to make a new custom their ought to be consent from the Cohanim.
[8]
In a situation where a yisroel was called up if it was done purposely then the aliya does not count.
[9] If it was done mistakenly then if the yisroel started the actual brachos he continues there.
[10]
Yet this is all when the shul is a public shul however if the shul is privately owned where we find regarding private shuls that gdolie yisroel gave in certain instances the first Aliyah to a yisroel without asking the Cohen to leave, as everyone who comes to that shul does so on condition that he follows the rules of it owners (yet this should not be done on a permanent basis).
[11]
[1] ויקרא פכ”א פסוק ח’.
[2] גיטין דף נ”ט.
[3] ראה משנ”ב או”ח סי’ קל”ה ס”ט.
[4] שולחן ערוך הרב סי’ קכ”ח סעיף ס’.
[5] שולחן ערוך הרב סימן ס”ו ס”ו.
[6] ראה משנ”ב סי’ קל”ה סקי”ח.
[7] ראה משנ”ב סי’ קל”ה סקי”ח.
[8] שם, שו”ת חת”ס ח”א סי’ כ”ד.
[9] ראה פסק”ת סי’ קל”ה סקט”ז.
[10] ראה שו”ע או”ח סי’ קל”ה ס”ו.
[11] ראה פסק”ת סי’ קל”ה סק”ט הע’ 59.