I read the first part as follows:
WTBTS was asking for no seizing or restricting of their assets while the appeal process goes through. They wanted NO enforcement of the judgement against them because it may be eliminated or reduced or modified during appeal. They further asked that plaintiff "Jane Doe" make no objections to such a request as long as she is protected from them trying to redistribute their assets (perhaps overseas) in order to say "We don't have your money."
However, the plaintiff would only agree to the "stay of execution" on the order to pay IF WTBTS would freeze all their assets, including any transfer of properties.
The plaintiff is saying that there really is no protection of her judgement without locking down their assets. I have to agree because their liquid assets are easily moved and the only thing left is the property.
Skipping all the back-and-forth legal talk, it sounds like the judge agrees to stay the execution of the payment, but also agrees to the plaintiff's request that properties not change hands. Still, the handwritten part sounds like it will leave WTBTS enough leeway to sell said properties if they get court-permission. All they have to do is show intent to be able to pay judgement and show intent not to move all of their NY assets out of NY. If a sale went through, they probably would have to keep the liquid assets within the NY corporation.
I think WTBTS would be crazy to come up with further liquid assets right now via the sale of properties. An appeal could modify the award to a greater number, with further proof that they have the liquid assets from the sale of properties. I would think they are not only working on an appeal, but working on offering a settlement that would avoid appeal so that they can pay a smaller amount (say $10million) and just get on with putting this to rest. Otherwise, their necks are way out there on a chopping block.