Trump has a huge advantage in filing a lawsuit over eligibility at this point. Not only does he have standing, which usually derails this type of challenge, he also gets to pick his forum. Trump can literally have his attorneys study every district court and every circuit court of appeals in the country, decide which of them is most likely to rule in his favor, and file his suit there. Since the SCOTUS is now shorthanded and liable to 4:4 rulings, allowing the lower court’s ruling to stand, the case will likely end in the circuit of Trump’s choosing.
If Cruz wants to remove some or all of those to Federal Courts, let him.