Suspending a Nichrome Heated Coil?
Between the two options of a self-supporting heated element, and a supported heating element, the self-supporting one will have lower mass, so will heat faster. 

Self-supporting means short and fat, so unfortunately low resistance. However, there are lots of designs, and maybe modules, to get low voltage high current from 12 V sources, think low voltage 100 amp supplies to CPUs and GPUs. 

I'd go with sourcing some thin stainless steel sheet, which has an astonishingly high resistivity, and cutting some into an inverted 'V' shape. Clamp the two arms between two bolts, the pointy bit would then point up and be able to penetrate into the bottom of the rocket, achieving good contact with the fuel. The bolts would need to pass through ceramic or glass, but maybe you could use GRP and face it with mica or something to survive the short, albeit intense, launch heat. I've been using some fake roofing 'slate' recently as a flame baffle in a propane kiln, and that seems to hold up well.

This would be a design for an intermediate life element, robust enough to serve several launches, but cheap and sufficiently easily replaced to not have to be built to survive 100s of them.