Well... yes, of course, PCR is inexpensive (about $7.45 per primer [30nt]) and effective... however... DESIGNING primers is EXTREMELY difficult, considering that the genomes of these species have not (to my knowledge) been sequenced at this point in time. While the protein sequence of the tyr gene is likely highly conserved in eukaryotic organisms, this does not in fact mean that the nucleotide sequence is conserved... (degenerative genetic code, codon bias, etc). In addition, you would need to design primers specific to each species, since they will not be the same.
I see what you are saying but I do not agree that it would be as difficult as you think. If you align Rattus tyr vs. Mus tyr you have 92% identity. I find it hard to believe that ball vs. carpet is going to show a massive deviation when you consider that they are at least as close to one another as Rattus are to Mus (possibly more closely related because Rattus x Mus hybrids always die before reaching more than a dozen divisions...) Similarly, if you align Homo vs. Rattus or Homo vs. Mus you have 83% and 84% identity respectively, primarily over the first 1800 nucleotides. That is still a large degree of alignment.
Now, I accept that balls and carpets, being reptiles, are rather more distant from Rattus/Mus than Rattus/Mus are from Homo but when you still see a huge degree of identity over 1800nt then it is a fair guess that you could use known sequences to generate somewhat degenerate primers that could work. And with the impending release of the Xenopus genome you could probably get closer using sequence from that. If you were feeling adventurous you could probably use the degenerate primers to run out a primer extension and get a more exact sequence to design specific primers with. Slightly more time consuming but still a relatively simple process for your average gene freak.
You clearly have a fairly decent understanding of molecular biology... just out of curiosity, are you a student/graduate?
I am a little further along than student