Requiring a specific tech level would do much the same as atternating armor and weapons
Unfortunately, the tech tree doesn't work like that. It's just simple prerequisites.
Padded armor needs to come with the equipment tech
Agreed; armor generally needs to come earlier in the tech tree, because right now you have to wait WAY too long for your first piece of armour. Heck, you can have bows researched by that time (and you have the master archer trait... they're already walking all over your enemies by this point)