The real concern is your exposure to xrays. The plastic housings provided a substantial amount of shielding. That's why those xray aprons you wore at the dentist were made of plastic. The lead was to simply keep them in position.
You may get lucky and your cabinet design will manage to neutralize the xray emissions through what's called the fairaday effect, but it's hard to be certain without very expensive equipment not available at the consumer level.
Oddly enough, one of the early signs of xray poisoning are changes in your digestive system as various bacteria are killed off and a new gut biome takes over. This will most readily manifest in changes to the color of your feces. I suggest that you take some documentary photos now, perhaps even upload them here just to make sure they're backed up, and compare after 2-3 weeks of exposure.
Should you find a change, luckily the effects can be reversed in time and you'll probably be back to normal in a couple of years.
Stay vigilant.