Our unit has a policy for everyone--RN, NNP, MD--3 tries per customer, that's it.
Use any vein--saphenous, antecub, scalp. Not usually jugulars or stuff they need for major surgery.
After as many attempts as you are describing (actually quite a few less), I'd have called it quits, given that particular dose(s) IM, made SURE the kid got plenty of PO fluids, and tried again for the next dose. Sometimes the baby is dehydrated, and you can't get a good enough flow to thread--did you try "flushing" it in? Probably you did.
Transilluminators help some people, not me.
I'm older, and I need bifocals, but they aren't strong enough for IV's and urinary catheters. I bought a $10 pair of drugstore reading glasses, put them on (on top of my regular glasses) to help with those tasks. All of a sudden, all the older crowd in the nursery keeps "borrowing" my magic IV starting glasses!!! Looks VERY dorky, but works great. So, if you're in that age group, you might want to give it a try.