Wow, I think a fast track to the endo would be ideal. Could your primary help with that. Hypoclgycemia can become a medical emergency. I believe, being diabetic would be a higher number, not lower. Clearly there is an issue with blood sugar regulation . People with diabetes can have hypoglycemia but I'm not sure there is any indication of that with you. I think you need to be seen as soon as possible to unravel this. https://www.mayoclinic.org/diseases-conditions/hypoglycemia/symptoms-causes/syc-20373685 There is something called reactive hypoglycemia. In people without diabetes, hypoglycemia can result from the body producing too much insulin after a meal, causing blood sugar levels to drop. This is called reactive hypoglycemia. Reactive hypoglycemia can be an early sign of diabetes. https://www.diabetes.org/diabetes/medication-management/blood-glucose-testing-and-control/hypoglycemia
Blood sugars in the 80s are actually totally normal. The fastings of 50 are on the low side. Most adults rarely go below 70, though children can be considerably lower and readings in the 60s are not abnromal for them.
Paradoxically, you may do better on a lower carb, higher protein diet. This is because by reducing carbs, you also reduce your panceas' insulin outputs... and it is the insulin outputs (maybe overproduction) that could be driving your nighttime and fasting levels so low. You day time levels seem to be normal.
The low nighttime levels may also be due to an over response to fasting. During fasting the liver produces glucose and the pancreas continues to put out insulin... In your case it may be that the pancreas is putting out more insulin than the liver's glucose production requires and hence the low numbers. You may find that a bedtime protein snack may help prevent you going so low overnight. Protein can slowly convert to glucose but has relatively less impact on insulin levels compared to carbs... you may also need to eat either breakfast (or a snack), again consider higher protein not higher carb, soon after waking to keep levels normal.
Many people who eventually develop diabetes do report early history of hypoglycemia... so continuing to watch blood sugar levels will be wise.
Hope this is helpful.