4:45?! Ouch. You have my sympathies.

You've got three options:

1. Wake by soft alarm (quiet/vibrating), stay in bed, do a wake-back-to-bed ritual (such as imagining and performing reality checks, recalling your last dream, etc). This is essentially a wake-back-to-bed, only it should be less intrusive as far as sleep quality goes.

2. WILD while taking naps. With a schedule like that, you could probably use a daily nap anyway.

3. Switch to DILD. This will have the least impact on both your sleep and waking schedule.