That is a gorgeous classic bike and should stay exactly as it is. It would be terrible to use a riser stem to torture this classy vintage racer into a sit up and beg riding position. So your task, pedalwan, will be to build fitness until you are worthy of the bike.

Okay that is hyperbole, but I do think the answer is to become a stronger, more flexible rider, not to modify the bike to accomodate a weaker, less flexible rider.

Ride more, during those rides vary your position - a few minutes on the tops of the bars, a few on the hoods, a few in the drops - and over time you'll build core strength and flexibility. When you are in the drops, ride harder and in a bigger (harder) gear - the downward force on the pedals helps support your torso and takes some weight off your hands. When you are on the tops, relax in a smaller (easier) gear.

This all assumes the bike is the correct size for you. Which we don't know. If you don't feel better on the bike in another few hundred miles, maybe post selfies on the bike, in the "Fitting" forum, and get fit opinions.