For reference - 1 ml equals 100 units of insulin.
If it is legal to buy insulin syringes over-the-counter in your State, then go to your drug store and ask for insulin syringes that hold 30 units of insulin or 1/3 ml.
You are using insulin syringes that hold 100 units or 1 ml.
The barrel is actually much more narrow in the 30 unit size. Therefore it is MUCH easier to measure to 3 units or 0.03 ml. The little lines aren't so little.
This smaller insulin syringe is designed for these smaller doses.
Here in Florida, we have insulin syringes that measure in one-half units. SO, you could even measure to 0.035 ml (for example) by going to 3.5 units on the one-half unit syringe. These were designed for pediatric diabetics but are ideal for dosing small animals as well.
If you are really struggling and cannot get the small syringes where you are, I'd be happy to mail you some 
Good Luck!
Sharla