I suggest you look at UltraCart (
www.ultracart.com). It's an extremely feature rich hosted shopping cart with I think matches
every item on your wish list with the possible exception of "Have the ability to integrate with sites like eBay, Shopzilla, Shopping, NexTag, etc.". UltraCart creates automatic Froogle datafeeds and may integrate with some of your other targets. It can also serve as the checkout engine for an eBay or Yahoo auction or the fulfillment vehicle for Amazon Seller Central sales.
In addition to the features you're looking for, UltraCart offers a number of additional features:
1) Suggested companion products.
2) Embedded catalog search engine.
3) Digital goods support.
4) Multiple tax jurisdiction support (down to individual counties or cities).
5) Gift support including multiple ship to addresses and choice of wrapping paper.
6) Packing support which automatically selects the best shipping box for a single item order or computes the minimum number and optimum size shipping boxes for multiple item orders (this is a great feature).
7) Electronic check support (in addition to PayPal, all major credit cards and all major payment gateways).
8) Volume discounts and contract pricing support.
9) Accounts receivable support for selected customers.
10) QuickBooks integration.
11) Built-in live chat.
12) Search engine friendly pages.
13) Contribution support.
14) Integration with major third-party fulfillment services.
15) Automatic reorder support.
16) SSL certificate included.
17) Custom DNS option.
18) Documented API to allow your own add-ons.
19) Multiple site support through a single back office (including individually branded shopping carts for each site). The user templating function is very powerful and easy to use.
I also find UltraCart very reasonably priced (up to 50 products is $35 per month, 250 products is $50, 500 products is $65, etc.). There are only a few extra cost add-ons (live chat ($15 month), Froogle datafeed ($1 to $10 month), E-mail marketing ($.0025 per E-mail), and digital content delivery ($6 per GB)).
I've used UltraCart for almost three years on a number of sites and have never had a problem. The support is great. The technical staff is also very receptive to new feature requests.
Hope this helps.