The $1,500 cash back listed on Cars.com and $1,500 conquest are only applicable for leases. If you look, they have a (1) next to them and the description given by cars.com for (1) is "Cash provided by the manufacturer to be put toward the customer’s lease". So no, the $3k described is only for leases and not outright purchases.
As far as what price you could negotiate on a tech package, I can't really tell you. I didn't shop or research for that package, but for my ultimate I negotiated a price about $1,800 under invoice before incentives. I went back and forth with several dealers competing against each other to get there. You should always negotiate without taking into account incentives since the incentives are from the manufacturer directly and not the dealer (i.e. a sticker purchase less incentives is still a sticker sale for the dealer).
These days, negotiating a "cash" purchase for a car will likely result in a higher cost for the car, if anything. The dealership must make all their profit on the car price (and warranty/etc) if it is a cash deal whereas a financed or lease deal also makes the dealership money on the back end which may make them more willing to sell the car for a smaller amount of profit. In a cash deal, the dealership sells the car to you; a loan, it sells it to the bank or finance institution; a lease it sells it to the leasing company - it doesn't really matter to the dealer, except that they get a kickback from the in house financing/leasing and from some local CUs that they work with. To me a dealer who is making money through the financing would be more likely to move on the price of the car, but that is just my 2 cents.
I would suggest you start your price research at truecar.com where you can build the car you want, see invoice, MSRP, and average selling price for the car with that build.
