First, a bit of background info. When you enable "Let buyer edit price" without Variants, the item's regular Price becomes the Minimum Price (which buyers cannot undercut), and the Suggested Price (which prefills the price amount when the item is added to cart) is accomplished by adding an extra amount to that Min. Price, using an &amount=X.XX parameter (where X.XX is the extra amount) tacked onto the cart button's href= or action= URL -- e.g., that URL for an item with a Sug. Price of $20 more than its Min. Price would look like this example:
For products using Variants together with "Let buyer edit price", the price you define for each Variant becomes the Min. Price for that Variant. In this case, there isn't a setting in Admin for Sug. Price, but you can do it manually by tacking that &amount=X.XX parameter onto the cart button's action= URL, as shown in the example above.
Unfortunately, this approach means the Sug. Price will always be greater than the Min. Price by the same flat amount for each Variant -- i.e., you can't have a larger/smaller spread between Sug. vs. Min. Prices for some Variants than others. One way around this would be to convert your Variants menu code into separate Add to Cart buttons for every possible combination of option values, so you could give each button its own &amount=X.XX parameter. This could become a bit tedious to set up if you have multiple options or many values for each option, but this tutorial walks you through the process: