I've always thought / said that "心底から申し上げる" means "I am saying this with highest level of sincerity (bottom of my heart)"
"心底から申し上げて、お詫びいたします。" I very sorry for what I have done.
Google search says "心底から申し上げる" is used only 650 times, which suggests 心底 and 申し上げる is very rare and not a natural pairing of words.
So, if I want to express that apologies, respect, love, condolences are coming from my "inner most thoughts", "bottom of my heart", "not superficial", is there a word to substitute for "心底"? Is it so context based on each emotion, it is on a case by case basis and there's no simple answer?
And, what impressions does "心底から申し上げて、お詫びいたします。" give?