Congratulations at re-finding the joys of DIY, with a lathe and some brass, no less!
I do wonder, however, why you felt you needed to flip your part and drill from both ends separately? I'm thinking you should have been able to drill all the way through with the 3.5mm and then use that as the pilot hole to drill your 5.5mm to the proper depth from the same side, not having to turn the part around in you chuck.
Nothing wrong with the way you did it, but it did require changing your setup to some extent, which is where errors can creep in, so minimizing that possibility is often desirable.