Foundry spears + pin drill + brass wire = sorted!
Something I'd rather avoid, to be honest. I've done that before with Old Glory speartips, and they break off too easily.
For future reference, I've now found some suitable ones from Castaway Arts, as pictured below. I e-mailed them and they're willing to sell the spears separately. A tad expensive because of the shipping from Australia, but I think I'll have to live with it.

I also noticed Cannon Fodder Miniatures (another Aussie company) sell some broad-bladed spears, but I'm still waiting for them to e-mail me a picture.