How do I delete an iPad remotely after selling it so the new user can set it up?

See the "If you no longer have your iOS device" section of What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support

Possibly meet with the new owner and do it yourself directly on the device?

You're not screwed, but I'd follow the advice of FoxFifth. The device is in transit to the buyer, so it's in the interest you and the buyer to perform a complete reset of the device.

Your main concern is to safeguard your privacy. Change your passwords, and notify your contacts of the issue. The buyer will probably only want to use their new iPad, not your contacts or your personal software, if any.

Thanks for your clarification. You don't need access to your former iCloud account, but the iPad's new owner will want to erase the content. It's very easy to do.

I'd ask the buyer to do to the following steps:

1. Start up the iPad, and navigate to the Settings icon.

2. Tap on General. On the bottom of the screen, the user will find Reset.

3. There are six options, but the user will only want to use Erase All Content and Settings. This will completely erase the content, and leave you with a factory reset device.

Set up this way, the new user will be able to enter new settings for the device.

You are going to have to deal with this, you have sold them a locked device, if I were the buyer I would not accept that as the final word. Refund the money or unlock the device!

all you can do now is give them the password to unlock (change it after the unlock) or refund the money (after they return the device)

There isn't a way to make it useable without the password. I don't have any experience with what you did to remove it from your account but the quote below from iCloud: Remove your device from Find My iPhone describes what you apparently did and indicates that if it comes online again it would reappear in your Find My iPhone at iCloud.com

Click All Devices, select the offline device, then click Remove from Account. If you don’t see Remove from Account, click All Devices again, then click the Delete button next to the device.If the device comes online again, it will reappear in Find My iPhone. If your device reappears, turn off Find My iPhone on the device (follow the instructions above for removing a device by turning off Find My iPhone), or if it’s an iOS device and you no longer have it, follow the instructions below for removing an iOS device you no longer have.

If the screen isn't locked (and I doubt that you would have shipped it with a passcode locking the screen, but if you did you could give that to the new owner) have the new owner connect it to wi-fi. The link also has instructions on what you should then do: iCloud: Remove your device from Find My iPhone

If you have already removed the device from your account but the iPad is still requiring your iCloud password, then complete the following

Force the iPad into recovery mode - If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support

Restore the iPad to factory settings - Use iTunes to restore your iOS device to factory settings - Apple Support

Since you have already removed your device from your iCloud account, the iPad should not go into an Activation Lock when the restore completes.

Hope that helps

Just enumerating the options, not passing judgement.

YYou can't. It will have to be performed by him.

IF he forces the iPad into recovery mode, iTunes will prompt him to restore to factory settings

all of his problems will be solved at that point.

IF you have communication with him, as I assume you do, have him Google "Apple HT201263" and it will show him step by step how to complete the above mentioned steps.

ONce the iPad has been restored, HE WILL BE ABLE TO SET IT UP WITHOUT YOUR ACCOUNT INFORMATION.