Does the pigeonhole principle rule out the possibility of losslessly simulating a universe the size of our own?
No, the pigeonhole principle doesn't immediately imply that.  It might be true, but you'd need some additional reasoning to prove it.

For instance, you seem to be assuming that the way the simulation works is by separately simulating each simulated particle using one or more real particles, and that a single real particle cannot simulate more than one simulated particle. It's not obvious that either of these need to be true.  For instance, perhaps you can simulate K simulated particles using L real particles, using a complex algorithm that simulates them jointly without any clear mapping from simulated particles to real particles.  It's also not clear why we'd need to have $K \le L$; perhaps there is some algorithm where $L=K/2$ (say).  Some additional reasoning would be needed to rule out these possibilities -- the pigeonhole principle alone isn't enough.

It does seem like a plausible-ish sort of conclusion, under reasonable assumptions about your model of computation.  But I don't think it's that easy to prove.