TheothersteveS my experience was similar to yours. The 24ga wire I bought from Gallium Source via Amazon came annealed, and was a pleasure to handwrap with.
I have 28ga and 30ga from a different vendor (UnkamenSupplies on Etsy) which is super springy until you heat it. If I heat it until it loses its springiness, it then becomes too brittle to wrap around a mandrel.
I guess mine is annealed. It came from a jewellery supplier. I guess people use high grade Ti wire to avoid allergic reaction to silver etc. Somehow I would have thought springy was better for that purpose but who knows! Anyway, it bends and stays put. I screwed up last night. Actually took off a coil from atty, messed around and then put the same damn coil back on. Fixed it up a bit and fires like a champ! Having just been playing with work hardened Ni wire which is very springy indeed, this is a joy!!