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Design Patent does not cover the Utility

It generally depends on how much of what functions/structure would be claimed in the Utility that was shown in the design patent and how long it has been.  Generally, the Design patent does not disclose any Utility so it would not matter.

Design Patents protect the particular look and obvious artistic tweaks to it, however, when you start talking about abstract structural limitations like "oversized" then that is where the Utility begins giving you the real scope you want.  For your kind of product invention, the Design and Utility complement each other in protecting you in court.  Each are opposite in how they protect, and the Design is much easier to win than a Utility, but the real "monopoly" value is in the Utility.