[Mart]

I may be wrong, but that setup looks right. Long spring, long shackles, sway bar in place. The early cars are pretty stiffly sprung. I doubt you would deflect things much by "pressing on the fenders".
If you stand on the bumper and start jumping up and down you might be able to get some movement.

It is a bit tired and sagged, but that would not make it stiff. The spring is straight, so the ends won't splay any further out. It isn't on the bump stops either, so that's not the cause.

Maybe get someone to jump up and down on the bumper while you watch underneath to see what is happening??

If it really is very stiff it may be something to do with the shocks.

It might be that it is ok but you are not used to it??? Don't know your background (no offense).

Mart.