how long can tomato plants stay in 2" soil blocks?

I've started a bunch of tomato, pepper, and eggplant starts in 2" soil blocks ( 2 inches across, so 4" square and 8" cubic area.)

How long after seed starting can they stay in these? I'm not finding much online. Would it help if I watered them with fish emulsion?

I've got 300 of them, so I'd really rather not pot them up into the bigger cubes before setting them out.

How well can you keep them watered during the heat of the day?

Around here, it's common to grow tomatoes in 1.5 inch  "6 packs" for 6 to 7 weeks before planting out. By that time they are 5 to 7 inches tall. Two inch blocks hold about twice as much soil, so I'd expect that the plants could be even bigger.

I believe they can certainly stay in their 2" blocks a little longer. I start mine in 3" square pots and they are about a foot tall and were 7 weeks old this year when I planted them in the garden. Plant age and size going into the garden vary for me year to year based on the weather. I always start my tomato seeds indoors on february 15th and the almanac last frost date for me (zone 7a) is april 15th, but I had them planted in the garden on april 7th this year.  In my experience by 8 weeks old in the 3" pots they are already becoming root bound and it is high time for me to get them planted. I would certainly think you can let those plants get 5-7 inches tall in those 2" pots. And like Joseph mentioned, how well can you keep them from drying out? I myself would once a week randomly pull a couple out to see how the roots are doing and when you see roots going around in circles in their soil block, it's time to find them a new home. In regards to fish emulsion, that will perk them up and speed some growth but if you're trying to keep them in the 2" blocks longer before setting them out, maybe skip the emulsion. Keep an eye on the foliage and if the leaves are getting pale, or light yellow showing up on the older lower leaves, some emulsion may be in order to give them a little nutrient boost.