What you propose doesn’t seem correct. I’d use

Voici une solution que je crois être équilibrée.

None of your propositions sounds correct, but they are several alternatives: using qui and adding “je crois” as an incise, either at the end or in the middle of the sentence

… qui, je crois, est équilibrée

or

… qui est équilibrée, je crois

or using dont

… dont je crois qu’elle est équilibrée

though it sounds a bit awkward with croire, however, with the equivalent (here) penser, it would yield

… dont je pense qu’elle est équilibrée

which is how I would say it.

Your sentence contains a single relative clause, with one embedded interpolated clause. The most formal way of writing it is:

Which, I think, is balanced.

Which directly translates into French as:

qui, je crois, est équilibré.

The commas are less often dropped in French (it might happen if the nesting is too high), and it can as well be found at the end of the clause : qui est équilibré, je crois (or je pense).

Notice the small letter in the translation, because a relative sentence on its own isn’t standard in French. One would repeat the last noun or use a leading pronoun such as ce to refer to a full clause.

Last, Un francophone’s suggestion:

que je crois (être) équilibré.

can also, in some cases, be a perfectly fine translation, as it is much more common in French, compared to its English grammatical equivalent: “which I think (to be) balanced”.