Hi,
I really like your choice of wheels. I think upgrading old bikes is a great idea.
And on that note... if you need to... you can use a Nitto Technomic stem and
a new handlebar if you can't find something on Ebay. You can also contact Harris
Cyclery, they specialise in hard to find parts.

Another trick you can try is to raise the bars. As you raise the bar, it comes back towards you at the same time. Sometimes it really helps in this sort of situation.

Another trick that often helps in your situation is a seat post with no set back. This will
bring your saddle forward a bit; and bring you about a half inch closer to the bar.

The last trick is that they make handlebars with different reaches. You can buy one with a shorter reach to the drops.