Leave it alone.
The asbestos in VAT is non-friable and poses no hazard if you don't mess with it. No drilling through the tile, no sanding of the tiles, no aggressive buffing or cleaning of the tiles with scrubbing discs. Carpet contractors with Home Depot will refuse to install carpeting over top of the tile due to H-D's fear of legal liability but many other installers will install carpet over VAT floors.
Fill the missing tile gaps with floor leveling compound. Don't nail in new tack strips for carpeting unless you first apply a layer of Duct Tape or other sticky barrier under the strips to trap fugitive fibers potentially released by the nails.
You can apply VCT(vinyl composition tile) directly over the VAT (vinyl asbestos tile) with no legal consequences. All the Federal Asbestos Regulations apply to commercial and Industrial properties, not single family owner occupied residential.
Just don't do anything foolish and everything will be fine.
I ran the Asbestos Inventory and Remediation programs for one of the Big three automakers for years. I encountered the same issue as the Original Poster last year at my son's house in the Detroit area. I contacted my former business associates who are Licensed Asbestos Remediation and Industrial Hygienists, and asked their advice regarding the problem
The information I posted above is their comments, paraphrased.
Since the OP is also in Michigan it also applies to him/her. Other states may have more restrictive requirements for home owners, so check with local authorities before following my comments if you do not live in Michigan.