WTH is a #45 tap? You mean drill bit?
Places like MSC sell broken tap extractors. They don't always work.
The acid idea should work if you give it enough time. The blade will rot slower than the tap because it is stainless and the tap is not
I set up in a mill vice, from the back of the hole, and use old carbide cutters to drill them out from behind. Sometimes the cutter binds in the tap and screws it out, other times the tap stays frozen, but gets a hole through it, which facilitates busting it up from removal. Obviously you eat up cutters this way, but old dull cutters ain't good for much else.
I've been told that EDM (electrical discharge machining) was invented as a way of removing broken taps. It is now a very important manufacturing process used in the construction of injection molds and other things. Anyway, I've seen tap burners for sell, so perhaps you could find a machine shop with one and have the tap burned out with EDM.
Since I started using a fixture to hold my taps straight, and using Moly-dee tapping oil, I hardly ever break a tap. WD-40 is no tapping fluid, FYI