I've wanted to do something since some time

Say I'm in the process of doing something, or have just done something, which I wanted to do since a long time ago. How can I correctly express?

Referring to something you go to look at, for example, maybe a painting in an art gallery. I just saw the painting and say to my friend:
3年前から見に来たかった。

Does this sound natural? I'm concerned about the ending. 見に来たかった almost sounds like I wanted to see it but no longer have any desire to. Am I overthinking this? Taken literally, the sentence translates to "since three years ago, wanted to come see [something]". This sounds fine, but maybe to a Japanese ear it is incorrect.

The other possible solutions I've been thinking about:
3年前から見に来ていたい。
3年前から見に来たくている。

Both seem to translate as "since three years ago, been wanting to come and see" but I'm not sure which is better. Should I be using the past tense with the above?

I've just looked at the painting, and what I really want to say now is "I've been wanting to see that painting for three years".

Please help, I've tried really hard to wrap my head around this by myself, but I don't get it and I just have to ask. Thank you.

As I sat down to think how I would say that, this one came to mind:
3年前から見たいと思っていたんだ。
3年前から見たかったんだ。

I wonder if you are familiar already with the "...no da/desu" or "...n da/desu" expression I used above. This "...no da/desu" expression is used to explain a reason/background. So here you are telling your friend about the long-standing wish of yours, like a piece of background information.

If you don't know that construction yet, you could (to keep it simpler) also say:
3年前から見たいと思っていた。
3年前から見たかった。

Note that I dropped the part about "come" see something. The wish is about "seeing" something, so that part just fell away.

The "other possible solutions" you came up with don't quite work, because the first one sounds like you wanted to have arrived here already (thus be here) three years in advance of the picture available for viewing. The second one sounds like "I have been here to see it since 3 years ago."

Turning over the sentence in my mind, your first one:
3年前から見に来たかった
is fine. It's just if you ask it's natural, that construction I used, in this case:
3年前から見に来たかったんだ
...would sound more natural.

Thank you for the answer, I understood.

I know about this use of "no" and understand it perfectly when I read/hear it, but I still have great difficulty using it. Often after a conversation I find myself realising I could have used this construction and kicking myself over it.

Oh well, almost had it. Thanks again! :)

…見に来たかった or
…見たかった, both sound fine.

To me, the nuance of 来た is the distance (which is relative) traveled to see the exhibit. If you live in Osaka and the exhibit is in Tokyo, then 来た emphasizes the long distance traveled. But, again, what's long to you may not be to the others.