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HPL I am not an old school guy with that knowledge. I had bikes from the era but I train and race on modern stuff and I have a road, track, time trial and sprint bikes set up specifically for events. But that is me.
With respect to racing and getting started in time trials, it is always a good idea to race what you have. You may love racing / time trials or not. The general rule for racing time trials is that results are 80% legs, lungs and heart, 10% brain and 5% equipment. Body position dominates aerodynamics and head position is the most important aspect of body position once the hip angle is set. As a new racer, you really do not have to worry about any of that other than do not get hung up on equipment since it is a minor component of results. Equipment can be a fun part of time trials and one wants to optimize speed and equipment matters when the time spreads begin to collapse between competitors. I can generate a lot of speed out of not a lot of power and that is due to technical considerations and mental focus not physiology.
I would suggest inserting the stem post farther into the head tube if that is possible. There may be old school stems available that do not rise as high as yours. And I would get the old school drop bars that have a larger radius. The larger radius bars will lower the drop portion of the bar and give you a lower body position.
More than likely, your saddle is too low. Why would I suspect that? Most racers saddle height is set for road riding and spinning. A TT setup, the leg is extended more and the rider tends to shift / rotate forward. In the old school vernacular this is riding on the rivet that gets its name from the rivets that were in the old leather saddles.
Here is a picture of the man himself Merckx. You can see, he gets pretty low but he is also bending his elbows. That is a fast position but hard to hold for long periods of time.
I cannot speak to bar end shifters. I hate all that old school stuff and prefer that modern shifting. I have electronic shifting and it is safer and faster since shifting buttons can be installed for different hand positions and allow riders to keep their hands on the bars at all times. This is more important in mass start racing such as crits. Good luck. Maybe others have some ideas for your setup and shifting.