The Trial Court's Judgment Is Going to Kill Us (Figuratively). What to do?

It's a bird! It's a plane! It's supersedeas! The method described in Texas Rule of Appellate Procedure 24 can keep the winner in a trial court from enforcing judgment. It also tends to guarantee that the trial court loser will pay the judgment immediately if the appeal is lost. Appealing doesn't keep the appellee from executing the judgment. Many appeals, though, would be mooted if the appellant had to pay the judgment right away. If the appellant puts up something of value which would pay the judgment, the appellee can be prevented from enforcing the judgment. However, if the appeal be lost, the judgment would be satisfied (at least in part) by the thing of value's being turned over to the appellee.
The limitation of the required supersedeas amount to the lesser of half of the judgment debtor's net worth or 25 million dollars was a response to the multi-billion dollar Texaco v. Pennzoil judgment. Back in those days, a judgment creditor was supposed to put up twice the judgment's value.  Appellant's counsel in Texaco v. Pennzoil was able to show that there was not enough bonding capacity in the world for that big a judgment. The new rule is a great big mazel tov to any future judgment creditor who finds itself in Texaco's shoes.