OK, I"ll admit it. I'm stubborn. I won't give up on this sort of problem. Even though I really don't have time for it. So here's how I've persisted over a lot of years, with some success.
You really need to report all deficiencies you find, through whatever incident reporting system your facility utilizes, hopefully to quality, so that risk management comes into play. A lot of work for you, but it's the only way to get their attention sometimes or to get the attention of someone higher up who can make changes.
Do your research - check out their references, which will be nursing manuals, articles, etc. and see if they are compliant with those. Nursing standards of care and practice are everything to nursing management. They aren't much impressed w/ lab references unless there are regulatory teeth behind them. If you can throw specific regulatory references, do so. I tell them that if I'm cited during a CAP inspection, we're going to have an issue with TJC (truthfully) and that gets action here. Sometimes I have to use a back door approach. If there isn't a specific checklist item directly pointed at the problem, can you find something else that will help. Don't forget CLIA regs.
As David says, sometimes compromise is helpful. Are the expectations greater than the nursing standard of practice? If they are, that's not necessarily a bad thing, but you might get better compliance if you uncomplicate things a bit. Nurses do have heavy workloads. If you can give a little, they may meet you part way.
Education can be helpful - can you get the cooperation of your nursing education staff? CAP requires annual education for transfusion and recognition of reactions (which means I can say that we've got to do it to pass TJC). I ask them to stress that attention to vitals is a very important way to catch reactions and that adverse events have to be documented. And if you don't document, you can't prove one way or the other whether or not a reaction occurred. Whoever your inspectors are, check out the requirements for documentation and education.
My experience is that it will take a lengthy period of time for improvement and that 'continuous quality improvement' is going to be the mantra. Staff comes and goes so there are always new people to be educated and good habits will slip over time. It took me years to get buy in that we had a problem. Our first electronic flowsheet for transfusion documentation didn't have mandatory entry fields - I pushed for that and didn't get it because nursing management thought that it would 'set staff up for failure'. I found that puzzling, but had to work with what I got. I looked at patterns of deficiencies and looked for failures to follow policy and reported multiple examples. I directly emailed nurses for followup - 'Hi "name", I noticed that the "whatever was missing" was not documented on the flowsheet for your patient. Please be sure to document "whatever was missing" because it is important for regulatory compliance or patient safety or whatever reason sounded impressive. I cc'd their managers on these emails. Sometimes I cc'd an education staff member I work closely with and she makes sure that common problems are addressed as part of new nurse orientation. We now utilize a flowsheet (Epic) that does have mandatory entry fields (Yippee!). Once they've had time to settle in with the new Epic version and I've got our new blood bank system up, I'll start looking at data again and reporting problems. Can you ask someone in the lab to help you with the chart reviews or delegate some of the reviews? There are some young techs in my lab who are eager for extra responsibility - perfect project for them.