He talked about making Wyckoff attractive to people over the border in Queens, and to young people like his sons, Tomas, who jams with his band in Bushwick, and Gabriel, an actor, who is looking for an apartment there.

Like Mr. Garg, he began challenging hospital doctors who were billing patients privately.

But this month, some doctors revolted.

A lawyer who said she represented the medical staff circulated a “no confidence” letter to the trustees. The letter said Mr. Rodriguez should be removed because, among other reasons, his LinkedIn page said he had suffered from depression and had been healed by drugs after being abruptly fired from another job as chief executive.

Mr. Rodriguez said in an interview that he had had clinical depression years ago. He called the letter outrageous and evidence that a small, disgruntled group of doctors was resisting his efforts to bring about major changes at Wyckoff.

“I am acting against some physicians who are taking advantage of a system that people did not pay attention to,” he said.

The hospital recently sold the stretch limousine for $18,000; it had cost $33,000 eight months ago. It sold the Lincoln Town Car for $9,000 and hopes to get $18,000 for the Escalade.

Mr. Rodriguez proposed to stay at least six months, at an annualized salary of $500,000, with a guarantee of three months’ severance if his contract was not extended. He promised to work to keep the hospital open and independent, in defiance of the merger plan that his own panel had endorsed last year.