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.
我是这个意思。
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)
我是这个意思。
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':
我是这个意思。
*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]。
(我的、他的、这个)意思是,[这个问题还远远没有得到解决]。
(My, His, The) opinion/meaning is, [this problem is still a long way from being resolved].