It is probably possible to create hidden, P2P-based mining pool on this coin.
At first, all nodes are solo mining as it is today, using official client. Then, people start noticing that they have to wait more and more time to receive their rewards. The overall difficulty to mine a block is getting harder, because there are more and more people mining this coin.
To solve this problem and receive something more frequently, people start cooperating with each other to produce something together and share their reward. To do this in a P2P-based, fully decentralized way, people start producing shares. A share is just a valid block with easier difficulty. So anyone can just modify original client a bit and start producing shares. The algorithm to achieve this is quite simple: if block hash is below share-difficulty, it is a valid share and can be broadcasted to pool nodes. If it also meets network difficulty, it can be broadcasted to the whole network.
Because some people are probably going to destroy all mining pools they can find, everything should be done in secret. So, to start with, people are sending shares only to explicitly listed nodes and to nobody else. To prevent detecting it by some adversary node sending shares to mining pool, the acceptance of the share is not announced to anyone (even "trusted pool nodes") explicitly. When pool node receives some block meeting share-difficulty and not meeting network-difficulty, it should respond with "block invalid" message if asked by anyone, but it should notice that the share is valid and prepare some transaction paying some coins to the share-creator.
After getting some shares from some nodes, each pool node independently broadcasts transaction paying nodes their rewards. It is a normal transaction, so there is nothing that adversaries can do to prove that it is a payment from mining pool. Also, as a normal transaction, other nodes can receive and broadcast it, so tracing the first node that produced this transaction seems to be impossible. Any inputs can be used to produce this transaction and also such transactions can be coinjoined, so finding the creator in a M inputs to N outputs transaction when M and N are greater than two is not possible with 100% accuracy.
There is nothing to lose using this method. Every pool node is also solo mining, shares are produced in the same way as normal blocks, except they have easier difficulty. To prevent spam, every node should decide how many times easier this difficulty should be. It is also possible to do some performance testing and just collect blocks locally to determine how many times easier this share-difficulty should be. Because everything that is needed to produce the next block is the hash of the previous one, it is also possible to run one instance of the original client and attach to it from many mining clients, getting only previous block header (and maybe also pending transactions or some stuff similar to getblocktemplate in Bitcoin). It is probably also possible to create some stratum-like protocol and produce only data needed by block headers, shared with every connected node.
However, the simplest possible way is just sending blocks. It is compatible with all clients. So, the node is solo mining and sending some shares to some trusted nodes. At the beginning, it is possible to communicate with some other miners owned by the same miner. Later it is possible to trust someone for a while and send some shares to it. If after some time the node receives some coins, it is marking such node as trustworthy and still sending shares to it. If not, it is marking it as a solo-only node and choose another node. In this way it is possible to find modified clients in a P2P-way instead of some centralized way.
Because 2POW divides the proof of work into two phases. According to the conventional mining pool, miners submit lower-difficulty proof of work to the pool to get rewards. Then all miners only need to submit the lower-difficult proof of work in the first phase, instead of completing the entire 2POW. This is because Many less difficult tasks in the first phase will get more expected benefits than completing the entire 2POW.