Trakhak

'I don't want the hassel of all this using the cassete "in concert with the appropriate chainrings". Is there a simple, mechanically robust, economically viable solution along these lines?'

Many people have reported great satisfaction with the newer internal hub gear drivetrains, which are available in various configurations; the 7-speed versions look like a good choice. Low maintenance, simple operation, and only slightly lower efficiency than derailleur gear systems.

That, or replace your right crank arm with a single-chainring setup. Note that the single chainring must be compatible with derailleur chains (i.e., 3/32" rather than the 1/8" track chain standard size). Probably wouldn't cost much more than the single chainring that you may or may not be able to find, and this way, you'd be able to swap back and forth between the triple-ring crank and the single-ring crank with relatively little effort, assuming that the same bottom bracket spindle length works for both.

If you do go this route, you might want to leave the front derailleur in place, since using the single ring in front with 9 sprockets in back can lead to dumping the chain to the inside or outside.

Or, as several experienced posters have suggested, do a little reading on the Sheldon Brown site and practice using the gears the way they were designed to be used. It's easy, once you understand how they work.