You'll need a chromatography approach. With a column and a detector you will be able to see each of those 3 products as separate distinct products, and fraction appropriately. I do not believe there is an easier approach. Best of luck!

HPLC/FPLC with a size-exclusion column rated for that MW range will elute each of them separately, in the reverse order to the one you have just listed, and any decent instrument will be able to detect each peak (UV-280nm) and collect the three fractions for you automatically.

As far as getting single-labeled antibodies, it depends on your conjugation method, ratio of antibody to oligo, and many other factors. The only way to guarantee one per antibody, that I know of, is by the site-specific reduction of disulfide bonds and subsequent thiol linkage to the reduced cysteine (there is a UV-induced conjugation method that is extremely efficient). If you use your current method you can try lowering the ratio of oligo below 1:1, if you can recover your unlabeled antibodies through the aforementioned process, and repeat as needed. You'll still get some multiple conjugations but you can optimize your process to minimize their proportion, you can do some statistical mechanics calculations to approximate that Goldilocks zone. I usually just derive it empirically, because I'd rather do experiments than mathematical models, which is why I'm a chemist!

Check out the GlyCLICK conjugation technology from Genovis: https://www.genovis.com/products/glyclick/