Okay, the problem is the sheer amount of pipe you have in the underground layer. Pipelayer has to figure out which connectors in the underground are connected to which other connectors. The analysis is very easy when pipes are built one at a time. The new pipe is just connected to the adjacent one. When pipes are built in random order, they self-organize into groups, and then those groups have to merged into larger groups.
To keep from lagging the game, it only follows a few pipes per tick. Since you have literally 15,000 pipes in a solid mass for each of these reactors, for no reason, and your UPS is so low, it will likely take hours after a blueprint is placed for all the analysis to finish.
Use the minimum number of pipes underground to link up the connectors.
BTW, you can watch this happening if you turn on the "Show network IDs" option for Pipelayer, and watch what happens in the underground view as you build pipe. Pipelayer can't move fluids until all the connectors are in the same network, which means all the pipes show the same ID.