Good question. Because I have not really made this, my remark is just a hint.
Plugin
I think that your hope may be come true by making new page plugin using "example page" plugin as example. And you should output form of Ask page in your new page plugin.
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Advantage: Version up of Q2A is easy
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Disadvantage: Program making will be hard
Ask page : qa-include/qa-page-ask.php
Core hack
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Copy qa-include/qa-page-ask.php
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Paste as another file (e.g. qa-include/qa-page-ask2.php)
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Perform remodeling that you expect
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Hack qa_page_routing() in qa-include/qa-page.php
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Add link in Admin > Pages > "Add Link"
'ask' => 'qa-page-ask.php',
'ask2' => 'qa-page-ask2.php', // <<< Add routing
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Advantage: Program making is easy (?)
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Disadvantage: Version up of Q2A is hard
Of course there will be other approach.