1. You need a different Engineer.
2. I think this is a potentially very expensive problem. RFB has it right, you need to take easy, inexpensive steps to mitigate the problem and then force the builder to fix it.
Possibly we have the order reversed here -- go see a good Real Estate Attorney, and let him recommend an engineer. Someone who has dealt with construction defects previously will know the right engineers. Any attorney should give you a free hour.
As it has been noted an "as is" purchase does not absolve the builder from liability for hidden defects. This could very well be a hidden defect which only manifests itself in wet years. If you had the building inspected in a dry time and the inspector said "no big deal", all that means is that either he made a mistake, or it is only a big deal in wet years.
The bottom line is that there is a very good possibility that that he really does not "own" this problem, but that it belongs to the contractor. If I were the owner, I would be speaking with an engineer AND an attorney.
Another reason to talk to an attorney is the inspector InvestorGuy says looked at it, saw the water and said "it is no big deal". It seems to me that if the inspector was paid and if it turns out that what he said was "no big deal" is a big deal, then the inspector has liability for this. Maybe he has errors and omissions insurance, most professionals do. Anyway, another set of pockets to look into. And no issue of a warranty expiring.
I would advise against pumping concrete into the crawl space. A 7-sack mix is going to be lot stronger than the usual 4-sack mix and until you are 200% certain this is what is going to fix it, you should consider this as an irreversible step. Getting that out is going to be a long, backbreaking job if it is not the right way to go. Suppose an engineer ultimately says: "sump pump", but the place to put one is covered in 7-sack concrete...
Also, just because concrete can be pumped, it is not a self-leveling fluid when it comes out of the hose. It has a density just about twice that of water and a consistency like an underripe banana (without the peel).
You need to move the hose to distribute it, shovel it to repair the issues from not moving the hose perfectly, settle it with a vibrator, and level it with a scree board -- minimum. It would be better to float it afterwards.
I have pumped concrete, many times, and with 5 or six guys and good access to the job, 1600 sq ft would work out OK. With this kind of access it is going to be a nightmare.