Finally got the perfect run with Poppea. I think this might be the only build that will work. I experimented with a lot of builds and it seems that whip is necessary. In a previous run I won with holy wand instead of the cross but that run was just spectacularly lucky in that I received 3-4 chests. This run is more in line with the amount of chests I'd expect in a run. Cross should be more consistent in terms of damage for the 25 minute mark over magic wand, because you can't expect to get holy wand.
The critical points that made this run successful was the incredibly lucky pentagram proc at 3:01 of the run. This run is probably impossible without 3 lives at 25 minutes, so not dying at the 3 minute boss is crucial. Luck was also with me at the 5 minute mark, where I was able to get pentagram as an upgrade to wipe out that boss. At that point I knew the run was probably the best I was going to get.