Can I convert the existing contracts to Fixed Price to enable the closeout process?
There is nothing in the FAR or DFARS that prohibits you from doing that; just be sure to write a memorandum of negotiations to explain how you converted the cost plus amounts to fixed price, and especially how you determined the switch from fee to profit.
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I assume you will use an "incurred cost" method as the basis for justifying the price- but if there are issues on the cost side, you'd better be able to explain how you resolved them on the fixed price side. In other words, you should not do this conversion if there are legitimate issues about costs incurred, unless you are going to exclude them from the fixed price, or unless you can justify including them in the fixed price (and getting to close out is not a reason).