Under the water, the cheapest and most viable option for them is not going for Option 2 as you suggested - to leapfrog or even closing the gap with US's submarine technologies from several decades behind is not going to be cheap and requires time (maybe decades) and tremendous amount of investments in human capital, infrastructural, industrial and engineering level.
No, China is not going to do that. At least not in the short term. There is a simpler, and far more cost effective way that has proven over and over again its effectiveness!
Their most viable and cost effective strategy is to make smaller, extremely cheap SSNs in the hundreds - numerical superiority has always proven to be quite effective against technological superior opponents in the past - from WWII to Korean War to Vietnam War - by making SSN 1/10 or even 1/50 the current cost by reducing its size and armament, it can make it extremely dangerous for US SSN "wolf pack" to venture into a swarm of "hornets". It may even become the emergent new class of submarines (I would call them "Submarine fighters" or "fighter swarms"). This will make it extremely costly for the expensive US SSN to try to go into Chinese water both in term of the risk of asset loss and human capital loss, not to mention the tremendous damage it will incur for the US technological lead if even just one USN SSN is sunk near chinese water (even if it takes down 10 of the Chinese midget SSNs) - because the Chinese would then retrieve the wreck and debris and the technological secrets it holds which takes US decades to develop.
No, the US would not risk losing its technological edge and the tremendous amount of investment and human capitals it has put in it when it is faced with the risk of having its prized subs sunk near the chinese water.
EDIT: I just realized I replied to a post by Jeff that was 2 years old! LOL!!
Don't take this personally, but that is a silly idea. It is a strategy only suitable for a second tier world power with zero hope of ever catching up to international standards, ever.
It might take a while for China, but every time they introduce a new class, the gap is narrowed.
China isn't expecting or preparing for imminent war, so wasting vast amounts of resources building huge numbers of midget subs makes zero sense.
The strategy you suggest is more suitable for North Korea or Iran, and is amusingly enough, similar to the strategies they themselves are actually employing, only with midget conventional subs rather than nuclear. Is that where you got the idea?
The optimal strategy for China is the one China is currently pursuing - building small batches per class and rapidly moving from class to class, making improvements every time. It may take time, but China is in no hurry as Beijing and most of the world firmly believe time is very much on China's side.
In the meantime, China already could effect a sort of effective deterrence strategy with is large, modern SSK fleets. They don't have 10 times the USN sub fleet, but then only the most "optimistic" souls on earth would think a USN SSN could kill 10 PLAN Songs or Yuans before going down itself, especially if the PLAN employ wolf pack tactics.
In the medium term, China could easily achieve swarm numbers and employ swarm tactics not with midget subs, but with unmanned underwater combat verhicles (UUCVs).
That is the only scenario under which the tactics and exchange rates you suggest would be acceptable to modern China.