I don't mean to be rude, but a lot of what you are saying doesn't have any basis in the legal issues that are live in this case.
Your complaint about not following the process or "discarding" the rules is not an accurate characterisation. The EPL's procedural rules contain a power for a decision making body to extend or abridge any time limit. Either Southampton agreed to that, in which case there is no appeal. Or they did not agree but the decision making body nevertheless abridged time. If that is the case they are possibly already out of time to challenge the abridgement. Even if they are not, they would have to show that no reasonable decision maker could have come to the same conclusion. To put it another way, the appeal would have to decide that every reasonable decision maker would not have abridged time. Not impossible, but not far off impossible in a context where, because of when Southampton chose to cheat, time was most definitely of the essence.
Your comments about separate court proceedings are also incorrect. The EFL Regulations contain a valid arbitration agreement and Southampton have already submitted to its jurisdiction. The power of a Court to interfere in those circumstances are very, very limited and only exercised in fairly exceptional circumstances.
Again, while it is not impossible to get an interim injunction to restrain the enforcement of an abitral award pending a claim to overturn it, such applications are vanishingly rare, particularly in circumstances where the arbitration agreement contains a provision about making an application to suspend an award pending an appeal and no application appears to have been made to the arbitration panel. Interim injunctions also have a huge downside in that to get one, the applicant has to give an undertaking to the Court to comply with any order it might make in respect of damages if the injunction is later found to be wrongly granted. If Boro are not in the final because of an interim injunction that is later found to have been wrongly granted, Southampton could end up having to compensate Boro for the loss of the chance of PL revenue. This could run to many 10s of millions. This would be so even if Southampton lost the playoff final, because damages are not about what the wrong party gained. They are about what the right party lost.