I know what you mean about finding sand that is coarse enough. Even if you find "extra coarse sand", that means that 10-20% of the bag is as coarse as you want, and the rest just clogs up the soil mix even worse.
Part of the problem is that "sand" only goes up to at most 2 mm grains. That's smaller than 1/10th inch. When grains are larger than 2 mm, it is "grit", not "sand".
We want fine or medium grit, not coarse sand.
Perlite is easier to find than screened grit unless you can find chicken grit ("#2" or "cherrystone" crushed granite). Something like double-screened crushed rock would be good, if it isn't too expensive or loaded down with dust, sand and fines.
Personally, I have a bark fetish. Pine bark, fir bark, balsam bark. Shredded and screened - I do my own screening with hardware cloth.
It's hard to find clean, dry bark mulch, especially at Home depot where "bark mulch" means logyard trash and dirt stored damp so it ferments. My Lowes has a clean, dry bagged product called fine bark nuggets, very cheap. But I have to screen it and then re-grind the chunks with an electric lawn mower.
It's easy to get any size bark shreds and chips that you want. I like them larger than the coarsest Perlite.
One trick that I've used on shallow pots is to set the pot (or tray) on top of an absorbent pad like a towel, Tee short, denim, or cotton flannel.
The pad has to TOUCH the soil mix or sand THROUGH the holes in the bottom of the pot.
If the sand layer doesn't break the wicking, that towel will pull the perched water out of the bottom of the pot. Then the rest of the excessive water will be pulled down to the bottom, and into the towel.
If you drape one end of the towel or pad over the edge of the shelf and then let it hang down 12", the excess water won't saturate the towel and stop flowing. Instead it will drip and evaporate until the only water left in the pot is capillary water (not perched water). In a water-retentive mix, that's plenty of water.
If the mix had been almost fast-draining enough, adding a wick might have made you water it more often.