You probably already know this, but if you go for more blood tests, make sure they are at the same lab. Results can differ for many reasons between labs.

I felt really bad the first 12 months of sobriety. Lots of things were wrong with me. I had a series of blood tests (every 3 months on average) done, learned about the important results, and kept a spreadsheet with those results.

One result is a snapshot, when you have 3 or more it's easier to see trends, and possible solutions a doc might not directly think of. Example: my uric acid levels were really high after 9 months. Doc would have thought it might be a result of drinking still, but as I was sober, and saw it going up, I ended up thinking about sugar (well, fructose...) consumption. Discussed that with the GP, she agreed, I took action (diet), and felt a lot better. That's not "anti-science" or negative towards docs: sometimes we need to be our own detective, piece information together, and discuss that with the GP.

Mind you, I'm not advocating "wild googling of ailments", but I know you wouldn't do that anyway. Just supporting your idea that you ideally want to be on top of this information, and discuss possible problems that you may see from those panels.