I don't think it's so much doing "wrong" as it is that not enough is done, so in answer to your 2nd question, yes, you need to do differently. If you are posting in the correct forum, that is, Ride Board: Animals Needing Transport, it's a good start. Double check that you're in the Ride Board Forum. Also, don't keep re-posting. Once is all it takes. If you need to make revisions use the edit button instead.
You MUST name the origin and destination in the subject line. In looking at your posts, none of your requests contain that information. BE PRECISE about locations; central Jersey is not a city so it doesn't help a pilot decide whether he or she can be of assistance.
You MUST check your posts several times a day. You actually received offers from two pilots the very same day you posted a request about 6 pups. Not checking in lost you that transport.
You need an idea of routing and how many legs a transport will require. Divide the total nautical miles by 300 (the average leg is 250-300nm) to determine how many pilots you'll need. Transports longer than 700 nm may require an overnight foster so be sure you have volunteers available along the route for that, and for getting dogs to/from airports. If dogs need pulled from shelters you will have to arrange for that yourself with local volunteers or the shelter; nobody here pulls animals on behalf of rescue organizations.
Contact pilots directly rather than simply waiting for them to read your posts. Know the routing and look for pilots every 300nm along that path. Note that commercial airports are rarely used; look for public municipal airports.
Sign your posts so pilots will know with whom they're communicating.
There's more but the above can get you started in the right direction. Additional information can be found in the Rescue Forum and by clicking on "rescue" in the menu near the top of the page.
Best wishes; I hope this information helps. You're welcome to email me privately if you have other questions.