The fact that the first DCA has returned the alleged debt to Barclaycard after letter1 should tell you that they had not a lot to go on so it will be the same with further DCAs who get ever more desparate and cheap the further down the line you go.
No matter what Barclaycard say about refusing to further contact you ask them for proof of debt including original signed credit agreements etc. by means of the three letters. Just modify the letters so they do not ask for proof of assignment or make reference to third parties etc. and follow the same procedure regarding timescales. You are legally entitled to the requested information proving the alleged debt before you are required to do anything.
Also start the three letters with any further DCAs that may contact you. Credit solutions have had their fingers burnt numerous times and will return the debt to Barclaycard if you stay firm on your position regarding a deed of assignment etc. Then Barclaycard will have to contact you or give it up as a lost cause. You may find that Barclaycard will write off the alleged debt rather than jump through hoops or enter into a tacit agreement then you can sit back and laugh at anything the DCAs send you because how incompetent would they look at any court when you produced the evidence that there was no debt direct from the source of the alleged debt. It is not your job to supply any such evidence to the DCAs as Barclaycard should have done that. Let them waste their time and money chasing a non existant debt.
I have had a recent letter from a DCA called ARC (Europe) Ltd stating that on the direct orders of their client and the fact that I had been less than cooperative regarding their enquiries

they would be putting the matter to the courts unless I confirmed the amount outstanding and paid it in full. This all depsite the fact that I had received four days previously a letter from the original company alleging the debt stating that the matter had been closed with no outstanding monies owed. The OFT, the FSA, and the CSA now have copies of the relevant correspondence and the police are currently investigating my allegations against ARC for attempting to extort money with menaces.
The early bird gets nicked by the VAT man.
Never appear at your place of work before noon.
Inland Revenue inspectors like to keep their afternoons free for paperwork.