I finished transplanting all of the Roma tomato seedlings into larger cups today.
Most of them seem to be handling the move pretty well so far. I also had to thin them out as I transplanted them. Some of the peat pellets had four or even five tomato seedlings growing in them. I used scissors to cut off the weaker looking plants right at the top of the soil.
Some of these plants are getting pretty big already. The larger plants also look very sturdy so I think that they will be able to easily handle going outside when it is time to start transitioning them to the deck when the weather is warm enough.