Best as I can tell, they flat out do not care about needles in checked luggage, and I'm been going through with them for over 30 years. (I have type 1 diabetes.) The only time they questioned anything was back in the 1970s when I was using a non-disposable syringe and needle and had it packed in alcohol in a steel cylinder, and it was the steel cylinder which drew attention. In recent years most of my departures have been from LAX and TLH, and I think all the secondaries have been in TLH, never in LAX best I can remember (over the hill? what hill? I don't remember any hill).
I have a minimum of two bottles of insulin in my carry-on, and up to four (current and spare of two kinds of insulin). Occasionally I get told it will speed up the process if I separate them like toiletries, but that I'm not required to do so. I don't. At some times I may have up to about 30 ml of insulin preparation (97% water) and the amount I'm carrying doesn't seem to have any affect on whether I get secondaried. My daypack has lots of stuff in it, and this seems to matter more.
I think I've been secondaried for this less than once per 25 boardings, and as soon as they see the insulin bottle, they just shrug and go on. (Ironically not all insulin requires a prescription, but it's treated as such for screening purposes.) They look through the bag with syringes, insulin, test strips, meter, finger pricker, etc, and all they even look at is the insulin.
As for sharps, I just recap the syringe and toss it in garbage. This is controversial on some forums, but I've never seen one come apart in normal handling. You could just mark them and put them in a separate section of baggage or carry-on -- as I say, they will not trigger any investigation. Or take the suggestions earlier in the thread for dealing with sharps. I have very few to deal with, since I reuse them, which is safe with insulin but not in general with other meds.
Edward