In your xml package (default product.VariantsInRightBar.xml.config) for that area of text, find the SECOND area where it pulls the product variant price. Should be right around line 439 and look like this:
<xsl:value-of select="aspdnsf:GetVariantPrice(VariantID, number(HidePriceUntilCart), Price, SalePrice, ExtendedPrice, Points, $pSalesPromptName, TaxClassID)"/>
You're going to comment that out and replace it with a choose. You can't have it always fire the replacement, or it will act funky for non-customer level prices.
Code:
<xsl:choose>
<xsl:when test="/root/Runtime/CustomerLevelID>0">
<xsl:value-of select="concat(substring-before(aspdnsf:GetVariantPrice(VariantID, number(HidePriceUntilCart), Price, SalePrice, ExtendedPrice, Points, $pSalesPromptName, TaxClassID),'My Customer Level'),'My New Price Prompt ', substring-after(aspdnsf:GetVariantPrice(VariantID, number(HidePriceUntilCart), Price, SalePrice, ExtendedPrice, Points, $pSalesPromptName, TaxClassID),'My Customer Level'))" disable-output-escaping="yes" />
</xsl:when>
<xsl:otherwise>
<xsl:value-of select="aspdnsf:GetVariantPrice(VariantID, number(HidePriceUntilCart), Price, SalePrice, ExtendedPrice, Points, $pSalesPromptName, TaxClassID)"/>
</xsl:otherwise>
</xsl:choose>
Of course, change the 'My Customer Level' with exactly what you want to replace... both times. And change the 'My New Price Prompt' with what you want to say instead. How's that work for ya?