I hope this message finds you well. As a matter of legal course, all three options proposed by Corp B are legal so long as they do not infringe upon some other contractual right that is either obligated to your or to Firm A.
Corporation B does not have to keep you. To that point, I would be willing to bet that there is contractual language that allows them to stop using your service at any time if they feel unsatisfied. That is harsh, but it is the way the employment law
As such, Corporation B can choose to enact either of the three options that you have listed above. The third listed option appears to be the best for all parties involved in that they continue to have your services available without a break, you continue to have employment without a break and firm A continues to receive payment for facilitating your services. Business efficiencies, as you know, revolve largely around continuity. If you have the opportunity to speak with anyone at Corporation B about the issue, make the suggestion that option 3 is your preference and then explain your rational as it relates to continuity within their operation. Make them the point of the talk and what is best for them in view of the work you have performed up to this point and what you intend to do going forward. The by-product is your continued employment.
In summary, all three options are completely legal unless violative of some other contractual arrangement, which is probably unlikely. The third option is the best for you under the circumstances as well as for the other two parties as well, both legally and from a continuity standpoint.
Let me know if you have any additional questions or comments.
Best wishes going forward.