There's an updated Aussie PA38 with a low tail but otherwise identical. An up to date version with a more economical engine (not necessarily the rotax!) and perhaps a revised W+B schedule
would be ideal.
Basically for it to be a good trainer, it needs to be a reasonable handling beast but should be quite stable in pitch relative to the current LSAs that are quite twitchy in pitch. Light on fuel, the 0-235 is actually pretty good at this, it will almost certainly take UL91 if it's not already cleared for it but the new lightweight conti 0-200 would be a better engine than the rotax for the job of a trainer, I don't believe that reduction gearing is up to the constant hamfisted power changes required for a trainer.
But it just has to be tough, inside and especially the gear. It needs to put up with 800 hours a year of which 600 are circuits. Simple is the key.
Aeros would make it too expensive because the certification process will be more complicated. The simpler the better.