My vote too, is for too small of a bike.
I once built up/reconditioned/overhauled/restored an old Centurion Omega & did a 700x23c conversion. I normally ride 58cm & the Centurion fit about like a 53/54cm frame... Ridiculously twitchy & a royal PIA to ride. Being low & in the drops is the only thing that made it managable for the few times I rode it before it sold.
The weight high & above the rear wheel is likely the culprit. The weight distribution ought to be more centered between the front/rear (or at least more evenly distributed) than it is currently. One way of doing this is getting the proper designer intended fit, or getting a bigger bike.
At my shop, the default is bars highest the steerer will allow & upturned stem. This moves the weight back, makes the rider more upright & appeals to new riders...That of course translates to better sales. Hence, the reason we do it. Experienced riders just change it for their proper fit when the get home.
Slam that stem, get in the drops & tell us if the problem still exists. If so, swap it for the next larger frame.
Good luck.
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