Hi Robert,
I've seen the "insufficient access rights on cross-reference id" error fire when campaign membership is sent across and it's sent for the wrong object, i.e. a lead when the record is actually a contact or vice versa. I haven't looked into this in a while but it used to be that when Eloqua sent across a net new record that also had a campaign response linked to it to SFDC it would send the record over and since it didn't already have a contact id or lead id attached to it it would send membership over and would attempt to create the record both ways, inevitably the contact ID wouldn't exist and would fail so you'd get a cross reference error on it. If you test your integration calls (with the Test call) function and test it with a new lead sending just a single membership/response over it should work. The other thing is that Eloqua will only record a single response to a campaign and SFDC campaigns don't natively support multiple responses to a single campaign for a single record either so if you're trying to "update" membership with a new response type it might also fail.
In terms of where you update campaign member status, it's in the campaign association (internal events) and campaign member (external calls) sections that hold the out of the box calls - here are some screenshots, these should exist in any out-of-the-box instance of Eloqua and then you can modify to your hearts content.
Image may be NSFW.
Clik here to view.
Image may be NSFW.
Clik here to view.
As far as your question about the possibility of having multiple response types per campaign, I've seen that done in E9 because you defined campaign response at the campaign level, in E10 campaign responses are globally set so you might not be able to configure different response types per campaign on the Eloqua side but you could configure the "sent" and "responded" associations on the SFDC side differently per campaign without it impacting the Eloqua side as long as you're still sending "sent" or "responded" or whatever the status' are that are globally set in your instance of Eloqua over correctly.
Best,
Lauren
