If it makes you feel any better, the four independent panels that considered the Everton and Forest cases (and their appeals) were all chaired by judges or KCs and the remaining members were all judges, KCs, CAs and lawyers of various ilks.
There shouldn't really be any cause for concern on grounds of independence or undue influence.
The PL will be feeling the pressure you mentioned, though, hence Masters saying nothing at all very loudly this week. But rest easy. The case will be decided on the evidence presented by the PL and the counter-evidence presented by the club. My money, for many reasons on the most substantive allegations, is on the club.
However, to answer your question specifically: the panel's decision can be appealed to another three-man panel chosen by Rosen, then there are limited opportunities to take the case to arbitration and, finally, very limited opportunities (to the extent that it would be virtually impossible*) to go to a "real court". Hope that helps.
* On the other hand, a HHGTTG quote: "Then, one day, a student who had been left to sweep up after a particularly unsuccessful party found himself reasoning in this way: "If such a machine is a virtual impossibility, it must have finite improbability. So all I have to do, in order to make one, is to work out how exactly improbable it is, feed that figure into the finite improbability generator, give it a fresh cup of really hot tea... and turn it on!""
In this case, the finite improbability generator is a highly skilled and very expensive team of legal advisors who are grappling with the very problem of appeals, I would imagine. The tea is probably the same.
:)