Hi Rob,
No, the Garli Beagle version won't do what you want. I implemented that prototype version on top of Garli 1.0, but numerical precision issues turned out to be a big headache. So, it hasn't been updated and there is no partitioned Garli version that uses Beagle. The numerical precision turns out to be a big issue for ML inference because the likelihood surface has to be flat to optimize on it, while in a Bayesian context a little scoring inaccuracy that causes a wavy surface ends up not being much of an issue. So, Beagle is really great for the Bayesian programs.
So, there is probably not a particular Garli version that would be fastest for you, although I could probably give some recommendations on settings that would be the fastest and most appropriate for your particular datasets.
Cheers,
Derrick