To clarify, you would like one plan under ERISA that includes the self-funded medical, along with the fully insured benefit programs. The Administrator provided you with a SPD but not a plan Document.
In Determining what type of benefits are included in the ERISA plan, you must refer to the plan document instead of the SPD. It is possible to have multiple SPDs included within one single Plan Document. The Wrap SPD you have serves as the SPD as well as the Plan Document. Note this is along with insurance carrier certificates of coverage, booklets and policy literature. If you were to amend your existing plan and remove the fully insured medical part, while incorporating the separate SPD for the medical benefits, it would still be considered one plan for ERISA purposes.