Synthroid needs to be taken first thing in the morning, with a cup of water, 30-60 minutes before eating/drinking anything else. I take my thyroid medications first thing when I get up, then get ready for the day and by the time that's done, at least 30 minutes has gone by and I can go ahead and take the rest of my meds, have coffee and either eat breakfast, if I'm going to or leave for my morning walk.
If you did the something similar, you'd be able to take your Meformin with breakfast within a hour of when you take your thyroid medication.
If your BS are really high in the mornings, perhaps you're eating too many carbs for dinner or in the evening or eating too close to bedtime... I try not to eat within 3 hours of going to bed. Some studies have shown that it's best to have the largest meal of the day at either breakfast or lunch and have a light evening meal. This can also help if you have weight to lose.
You are obviously having a problem with fasting glucose. Maybe you can take your metformin at night with your evening meal and hopefully that will have a better effect on your fasting levels. This will also solve the problem of when to take your thyroid meds.
If your fasting levels still remain so high, even with metformin, you need to see your dr again for additional medications. You may need to consider insulin as an appropriate medication.
Low carb diet, particularly eating low carb at night may further help with blood sugar.
You can also look up "dawn phenomenon". Do you have a home meter? Are you checking blood sugars 2 hours after eating? How high do you go after eating?
I agree with Barb135. That is sound advice.
As to the Metformin, it appears you need as long talk with a diabetes nurse practicioner or nurse from a diabetic clinic to explain the nature of diabetes and your specific issues. Super_sally888 has also provided excellent advice, but medication decisions should be based upon inter-action with your physician. Diabetes is very complicated and most doctors take between three and five seconds to explain things to you. Then it becomes too embarrasing to admit you don't understand everything. You need a home meter and must resolve to take numerous readings, which must be recorded. Plus a record of exactly what you eat and when. Readings don't mean much except when correlated with food intake. With many meters the readings are recorded - and when you visit your diabetic nurse they are downloaded into his/her computer. There are some very good diabetes control programs, where you go to several sessions and they take time to make sure you understand everything about the illness. And your medications. As a general rule, it is important to maintain the same schedule with regards to medications, other things being equal. That is to say, the same time every day. This is too complicated an issue to be properly dealt with in an internet post. Good luck.