Know nothing about suspension and steering, should I attempt?

Have you replaced the tires in getting it ready for the road? If you haven't, that shake at speed could be flat spotted tires. If they haven't been replaced and spent any significant time sitting around it could mostly be a tire issue.

The fender braces, the ones that go from the firewall/cowl to the fenders, do help with that a little. Which is why the factory added them on the later cars. But what you're describing sounds like an issue with the tires/alignment/suspension, with the hood shake possibly exaggerated a little by the missing braces.