Is there a way to globally make the Constituent id replicate as the Member id in every record?

If you cant find a direct way, perhaps export all the members with the id numbers. Copy the column that has the constituent ids and paste into a new column. Then try to maybe import them, specifying the second column as the member ID.

Group all the members and export their Const ID, Const Import ID(Optional), Membership ID and Membership Import ID. Copy the Cons ID in Memberhsip ID column and then Import it back into the database. You  may have to use the import ID to identify the records in the system.

Note: If you have more than one membership you have to think about the ID structure for the membership. You cant use the same Bio ID all types of membership. If it is the same case with yours you may prefix or sufix the short form of Membership Category along with the Bio ID. Eg. 123456SUB/NSUB123456

Hope it helps