好问题！你提到的这种类似的句子还不少，在小说中很常见。我说一下我的看法，可能不正确，算是给出一个理解的思路。

“Singora, you are lovelier than the heroines of ancient times!" he cried, with what he thought was his most winning smile.（书名为“Barchester Towers”）

可以把he thought 理解为插入语，直接拿掉后变为“with what was his most winning smile”（名词从句）。with后面接的还是某种smile。这样解释就通了。

这里还有一个问题我提一下，就是为什么是“with what was his most winning smile”而不是““with what his most winning smile was”？这涉及到不同的词序表示的意义略有不同。因为有he thought的存在，所以用“with what was his most winning smile”是最合适的，表示的是分类：“他以为的最能代表他胜利的微笑的那种微笑”，而不是其他的某种微笑。

The New Cambridge English Course 3 Practice Book with Key这本书的第76页有这么一句：

With what he thought was tremendous presence of mind , he pulled on to the hard shoulder , stood up on the front seat and urinated into the flames. 

再列举一些小说中的类似例子：

He'd been thinking about this all afternoon, had in fact thought of nothing else, and he'd come up with what he thought was the most logical solution.（Baby With A Badge）

He was all too familiar with what he thought was one of the side effects of her wounds.(What's in a Name)

He came up with what he thought was a good idea.(The Short Stories of Steven Arnett)

He approached the woods with what he thought was an unwarranted trepidation.(MAMBO!)