[Chas]

Milkjug plastic?

Whatever is chosen for the spider, the material must be compatible with popular adhesives...

The speaker can be assembled with any modern adhesive that is available BUT, the assembly process for an apprentice will be slower with possible mistakes aggravated by premature curing or mess of adhesive...

OEM speakers up to as late as the "Hi-Fi" era were assembled with collodion, a solvent removable adhesive. Jigs and other devices speed-up assembly so "pot life" was no issue. For the apprentice re-coner, a jig to hold the voice coil perpendicular to the cone face may be required. Easily made from tubing and a flat of MDF...

Use of a solvent removable adhesive is a more appropriate material to use during re-coning. The adhesive can be used to pre-coat surfaces and let dry, unlike a Contact Adhesive, a solvent adhesive will glaze over and will not be tacky. Coating both surface to be adhered and allowed to dry. Then, pre-position, clip, clamp or fix by weight or position the locations for cone, spider and voice coil. Not all at once but build as an assembly. When fixed in position, flow the appropriate solvent and wait 1/2 hour, the solvent will melt the adhesive and fix the parts in the correct position. Remove all temporary fasteners and add additional adhesive in high torque areas like the spider to cone to voice coil joints. Allow to cure, pull shims and test. A disposable plastic eyedropper is very useful, that is why the viscosity of the adhesive is important too. Other collodion adhesive brands may work if they are appropriately thinned to flow like G-C speaker service cement.

A once popular solvent adhesive was G-C speaker service cement, however, it may be hard to find. Duco cement may work or not, collodion was used to coat airplane canvas and model paper surfaces, to adhere facial costumes and coat canoes.

Saving a electro-dynamic speaker is noble in that they are not making anymore, at least for the repairs of radios and most anything substituted will be mediocre at best.

YMMV

Chas