Screenshots
Blueprint
6 science packs are loaded on the red sushi belt, while 7th pack (either space or red depending on player's preference) is loaded on a dedicated yellow belt.I'm using buffer chests to control science pack production, but they're perfectly optional.
The entire system is designed to be built in early game and upgraded through the game as more science packs become available. The most important upgrade is the introduction of red sushi belt, everything else is pretty easy.
Sushi belt carries 6 packs in a tightly compressed setup. Blueprint is safe to be rotated, but keep in mind that the direction where science packs are coming from, and the sushi belt direction (counter-clockwise) are related - if you want to keep blueprint orientation but feed science packs from above, you will need to run the sushi belt in the opposite direction (i.e. clockwise).
How the sushi belt works:
Each science pack is put on the feeder belt's top lane - the lane which is "upstream" for the sushi belt. Circuit on the sushi belt tile will read it's contents, and when there's no science pack of the matching color, feeder belt will activate and put one of packs onto the sushi belt, immediately deactivating the feeder belt again until the pack travels to the next tile of sushi belt.
Eventually, each tile of the sushi belt should have 1 science pack of each color - that's 3 per lane. This works because inserted pack is fed "upstream" and has to travel the entire tile before next one of the same type can be inserted. This is why direction of science packs input is important - if we feed the packs via the "downstream" lane, it will only disable the feeder belt for a short moment as it will almost immediately leave for the next sushi belt tile. This will result in a dense stream of packs of the same color being fed, potentially starving other pack types from opportunity to feed into the belt.