Exporting Text to EPS Generates Separate/Overlapping Fill and Outline Text Layers?

When I export to EPS, the resulting document contains two layers for each text element - one for the fill, and another for the outline.  Though the color of the text outline is set to invisible in CorelDRAW, it appears in AI, for example, as a fine line, and the two overlapping layers can be edited (as text) separately.

I was hoping to collaborate with some AI users, but this makes the documents difficult to exchange (and exporting to AI format has even more problems).

Any ideas how to produce a more reliable EPS (or AI) export?

Any advice is appreciated.