That Korea Aerospace describes it as "accounting advice" is the killer. One excuse being so ridiculous reveals the others to be shams as well, even though in isolation "property consulting" or "insight" might have a veneer of plausibility.
But I suppose no excuse could work, given Essential was a shell company created in order to shuffle money around. Essential opened its bank accounts with lies, and the KYC rules for banks ("know your customer") expressly exist to prevent shuffling of money around. It had no employees, no premises, no marketing to try and win these clients eager for advice, not even a website. The only way AT&T and Novartis could have known about Essential Consultants is if they got told: pay here.
Giuliani tried to take the line that the Stormy Daniels was a private payment, unrelated to the campaign, something Cohen handled as Trump's private fixer. In that case, AT&T and Novartis paid huge amounts into a fund that was then used for Trump's private payment. AT&T is American, subject to US law, SEC regulations, US taxes. It's clearly a secret bribe - AT&T secretly funding the secret slush fund that had secretly paid off Trump's secret lover - at a time when AT&T was trying to get its Time Warner merger past the Trump administration's Justice Department and was trying to get net neutrality regulations repealed. I think AT&T are in deep ****.
Novartis is Swiss, not sure if being foreign helps or hinders their position. I haven't seen any explanation for why they made 4 payments of just under $100k. These payments weren't monthly instalments, they were made several days apart. Maybe $99k gets round some internal control their finance department has in place?
Trump has told so many lies about Stormy that we don't know how/if he reimbursed Cohen. Maybe these lies were forced upon him, because he contributed nothing to the $130,000 settlement and just used this bribe money to repay Cohen. Maybe there was money that flowed from the Essential bank account to Trump or another member of his crime family.
AT&T's best approach is to come clean. I'm sure that's what their lawyers are recommending. The biggest telecoms company in the world can't be seen to be hiding this sort of crap, even if what they did was technically legal. They should disclose all the paperwork and emails they received - invoices, who personally performed the "insight" work, who provided the bank account details to pay, who authorised it at their end. To be part of a cover up would be a bad mistake for a company that relies so much on regulation, lobbying and political influence.
This is all without getting into the Russian link.