How will a massive increase in hashpower affect orphan rates? Difficulty always lags behind a little. It is also limited in how large adjustments it makes each time. What if the (global) hashrate doubles overnight? What if it quadruples?

How much can we expect the orphan rate to go up? By orphans I mean blocks on a block chain fork other than the main chain (longest chain).

How large would the losses then be for PPS pools and other pools that pay for orphaned work, before the difficulty catches up?

What about a solo miner? What about P2pool? In both cases many of the miners may not be well connected to other block generating nodes on the bitcoin peer-to-peer network.

Perhaps there is useful information available from alt coins that have gone through something similar or just have a higher rate of block generation.

The question is of course motivated by the imminent shipment of ASIC-based mining equipment with hashpower that will dwarf anything seen so far. If you do an estimate, feel free to use any numbers you feel are realistic. I have no idea what amount of ASICs are currently going into production. The question could also apply to next generation ASICs, quantum computing or weaknesses that may be found in the SHA-256 hashing algorithm.
If the average time to find a block is T, and the typical time for a found block to propagate in the network is t, then the proportion of orphans among all blocks will be roughly 1/(1+T/t). As long as T>t there's not much risk for the network; however it could be a challenge for orphan-paying pools, for example If T=9t then 10% of the block rewards will need to be paid out of pocket.

If a PPS pool pays B/D per share, it is in fact using an artificially low difficulty - the difficulty metric measures how hard it is to find a block (orphan or not), when in fact what is relevant for calculating the due reward is how difficult it is to find a valid block.

If the network hashrate increases by a factor of X, then until difficulty catches up the average time for finding a block is (10 min)/X. I doubt the transition to ASIC will cause a discrepancy by a factor of over 10; this would give T = 1 min. With a conservative value of t=5 sec you will get about 7.7% loss for paying orphans. The actual numbers for both X and t will likely be much less (especially since concentrated hashrate lowers t), so I don't think the loss during the transition period will be prohibitive.