You dont mention the year or fork/frame material of your Allez Comp.
Owners of the same model/year/frame/bike could give you *much* better feedback if you share that data.

I own a 2011 Allez Elite carbon fork/ aluminum frame.
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Some ideas, in order of increasing expense:

Lower Tire Pressures, under 85 or 90, especially in front.
Some Gel bar tape, possibly double-wrapped or with pads under the tape. ( I prefer a firmer grip and feel, so not for me...).

Tires: 25 to 28(25s fit on my 2011 Allez Elite, but they measure almost 27)

Carbon Handlebars

A more modern Wheelset with a wider internal width...others can elaborate on how this effects 23/25/28 tires' size/shapes/profiles/overall circumfrences, and what internal widths to shop for...