"Does anyone know of a place to buy a 30 amp extension cord with built-in sockets for 15 amp appliances?" I doubt you will be able to find such a thing because it would be very dangerous. The wiring inside the appliance is not likely to be able to carry the fault current from a 30 A source long enough to trip a breaker. The wiring in the device will become the fuse in the event of a fault. You could take a small panel board and connect it using a 30 A cord and plug, and then wire 15 and 20 amp breakers and receptacles. Mount the panel to a section of plywood along with all the receptacles boxes.

Vintage silverplate platters just a bit larger than dinnerplates are remarkably inexpensive, given the rising price of silver and gold. Look at Goodwill, estate sales, garage sales. My generation (married late 60s early 70s) got this stuff for wedding presents, often because our cheap relatives got them at the bank when they made a savings deposit! The brides didn't want to keep them tarnish free so they put them away and now they're downsizing and their kids don't want to polish them either. I have two of them in a box destined for the Goodwill right now.

I suggest a local lighting/electrical supply store. Our electrician took quite a while installing the plug mold. I believe it is difficult to install. That's a good reason for you to have the electrician who will install it be involved in ordering it. They'll get the contractor discount if they get it locally. Also it's easier to return this kind of thing in person than online. The electrical supply store will know a lot about it and be able to give good advice.

Lots of good ideas. I investigated electrical code and the local code does not specifically prevent outlets in cabinets or drawers. Therefore, they are permitted. That opens up many possibilities. I do not like a flexible wire to a drawer. Under the sink is good for others, not for our particular family, but a really good inspiration. Now it seems a recessed medicine chest or niche would suit. Currently there is a mirror mounted flat to the wall. I could build a medicine chest with the mirror. Even better, a smaller recess on the wall next to the vanity with a door or mirror. ANY surface or cabinet will accumulate the maximum amount of sthuff. A small cabinet will attract less. Next project after tiling the bath surround is building a new vanity carcass with drawers, no doors. Everyone gets a drawer for their things. Aside: we have our first aid box and family medicines in a kitchen cabinet, not in the bathroom medicine cabinet. It allows a larger group of supplies and you don't have to interrupt the person in the bathroom for critical needs.