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It would make more sense to transfer your site to the new domain first. Get that working correctly and ranking as it should and then you can focus on changing the design. Here is some good information from Google on how to achieve this. -Andy

Yes, you will need to add some lines in your .htaccess file on the .net version pointing to the.com version using 301's. Will you lose any organic positions? If done correctly, you will maintain your rankings (minor fluctuations typically will happen).