Tier 5 visa - questoins URGENT- US citizen

Hello All - any insight would be appreciated!

So I am currently on a tier 5 visa (sponsored by an umbrella company BUNAC) and work for a start up tech company. However my contract with my current company ends in december and I have recently been offered a position from another tech company. The company holds a tier 2 sponsorship license but I dont think they are wanting to go through the process of sponsoring me for a tier 2. So I am looking to be sponsored by another umbrella company AIESEC - they provide the CoS. However when I told my new employer this and they brought the information to their lawyers, the lawyers mentioned something about insisting that I have to have tier 2 visa. Do most immigration lawyers know about the tier 5 visa? Do they know about these umbrella companies? I am just unsure of why he/she would deny me seeking out a sponsorship from this umbrella company that will provide a tier 5 visa, so that the company doesn't have to deal with it.

Another question, If I do go down the route of a tier 2 visa. I was told that since I am still a student I can bypass the labour market test? Has anyone dealt with this before? How difficult is it to obtain a tier 2 visa and not have to enter the labour market test?

Any information please!!