>> Is a 1020 tray the flat trays with no holes?
I think "1020" is just the size, like 11"x22". I wonder why they didn't call it an 1122 tray? You can get them with or without the slits. In fact, I just saw an ad for a 1020 web-bottom tray.
>> If it is, I tried putting my plug trays in them but they seem too tall and my sides bowed out.
For me it varied by brand which was taller, the tray or the inserts (or plug cells). It seemed that some were designed to hold the inserts (or the plugs) UP away from the floor of the tray. As if they wanted the cells to hold more water, and for roots to air-prune instead of growing into the trays. But when full of soil mix an atere4d, they sagged and touched the bottom anyway, or slipped off the 1020 wall in one corner. Or I just picked a bad combo of 10-20 tray and insert or plugs.
Anyway, now I like the 1020 trays with lower sides, and plug trays with deeper cells. I trimmed to rims off some plug trays so they would "sit". Also, I always cut my plug trays into thirds or quarters, so I turn them over and push root balls out with a dowel. (I'm clumsy.)
Do you do some plug trays smaller than the 128-cells? Wow. I guess only a few days go past between "the root is a tiny thread" and "the 200-cell is root bound already".
Have you ever tried a "20-row-tray"? That has 20 rows, each about 10.5" long, and maybe 1/2" wide at the top. The idea is to sow in the row every 1/2" or so, and then have a little less untangling to do when you pop the row and pot up.
