When you find Tamper Resistant plugmold, please let me know.
If the space behind the sink is 12” or more, according to 210.52[C], it is considered a single counter space and you would only need one receptacle for the entire island, regardless of it’s length.
If the space behind the sink is less than 12” then it is considered two separate counter spaces and you would then need two receptacles, one for each of the “separate” counter spaces. You can put more in if you want, but that is up to you.
I usually mount the receptacles on the ends, close to the working side of the island or peninsula. That would normally be the kitchen side, or in your case, probably whatever side your sink faces and the faucet is controlled from. Even with the countertop overhanging the base, putting the receptacle close to the edge of the working side of the island allows for less than 6” of overhang to get to the receptacle. Most inspectors understand the frustration of trying to comply with the NEC and the reality of island and peninsula design and receptacle installation.
I have also flush mounted the receptacles in the face of the base cabinet between drawers when space allowed, but sometimes it just isn’t possible.
Plugmold is an option, but I haven’t seen it in TR yet.