... If a microcontroller running compiled code is barely fast enough, should PICAXE even be considered?
PICAXE Charlieplexing ? - A very big YES !.
It's not the size of the matrix that matters, it's the number of simultaneous lit LEDs.
For example, a 'Pong' type game could be played on a big matrix, but maybe only needs a dozen LEDs lit at once. PICAXE could handle this.
A 'Black Box' ray-deducing game could have a huge grid, but only needs a few LEDs lit at once.
My orrery has 528 LEDS, but only nine are lit at once.
Another use is not as a dynamic refreshed graphic matrix, but as, say, the 49 numbers on a lottery machine, or the 99 numbers on a bingo card.
Or an LED above each key on a piano, showing which to press next.
There is no problem using a PICAXE to Charlieplex up to, at least, 30 simultaneous lit LEDs, no matter how big the matrix.
Give it a try. The 80 LED bargraph is a great starting point. Very easy to wire on a piece of stripboard, and easy to see the logic needed when programming.
Cheers,
Buzby