As long as other compnay is reay to sponsor you under valid H1B, thee should not be any problem in the H1B transfer. The current consulting firm can not do anything or hold your H1B for nothing, H1B is just a sponsorship to work, not a contract. In fact, job contract as such done by the so called consulting firm for their own benefits is illigal and void in US, and no need to worry even if they asked you to do contract while applying for the H1B. So go ahead with the extension and yes, ask your consulting firm to provide you the original of the H1B approval document from USCIS (which they normally do not provide you, in that case you can apply to the USCIS for a copy of it, but you should know your EAC number). Hope this works.