Tips for making fermented beets?

[opera]

Hi,
I am new to vegetable fermentation, but because of an exploding garden, have dived right in with several different veggies. Most of the veggies I've done up with a brine, garlic and dill. Cucumbers and green and yellow beans have turned out great, but some of the other veggies seemed to have some issues. In particular, the cubed beets. I have been refrigerating most of the ferments after 3-4 days on the counter (we've had really hot weather here), but I left the beets for over a week, as they still seemed hard. When I tasted them, the flavour seemed "off", and they were still hard. Tonight there was a not-so-pretty mold growing on the top, so I've ditched the batch. Are there special tips / tricks for doing fermented beets? Should I have sliced the beets really thin, or shredded them like sauerkraut? Thank you in advance for any suggestions -- I'm eager to try again, as there are lots more beets in the garden ready to go!