我 is not 'my' here.
A is OK as a short answer. B is OK, C is not good.
Lack of context confuses things.
意思：literally 'think think'
Simplify things, take away 真：我是这个意思。
这个意思 refers, points to an opinion, idea or meaning. Whether or not this opinion, idea or meaning is from 我 or was just adopted by 我 is not clear. 我 may just be concurring with someone else's opinion.
I 是 that thinkthink
I 是 that opinion/idea/meaning
Now swap things around:
这个意思是 [some meaning or opinion]。
这个意思是 [我]。(我 is not an idea or opinion, but a preceding context could legitimize this: 这个意思 points back to something said before.)
Even in a language with case, either side of 是 a noun is still nominative case. The sloppy Western Grammar idea of 'subject and object' cannot apply to 是。
You have 2 words in the category noun: 我 and 意思. Both and neither are 'subject'. Both are what you are talking about.
Is 我 the subject or a non-subject topic like a possessor? (i.e. my)
If 'subject' is 我:
我是这个意思。(This is why you want to impute a 'my' for 我: This structure won't work in English.)
I am this opinion. (but in English you must say: ‘I am of this opinion.’ or 'This is my opinion.' You are patently not 'this opinion'.)
If 我 is 'my':
*My is this opinion/meaning. (not such good English)
Explicitly state the meaning or opinion:
(我的、他的、这个)意思是 [some meaning or opinion]。
(My, His, The) opinion/meaning is, [this problem is still a long way from being resolved].