According to Google Books Ngram, the comparative "broker than" appears to have enjoyed some currency in the mid-1700s. Appears being the operative word though, because if we look at the results a very different story emerges.
First and foremost, the results recorded in that impressive red peak between 1750 and 1760 are false positives. There are no recorded instances of "broker than" in that period.
Secondly, all the recorded instances that appear between 1800 and 1930 use the term broker as a NOUN, not as an adjective. To give but a few examples:
If would, no doubt, rather play the part of a broker than “equalize the exchange (1819), they are oftener cashed by the broker than passed into currency (1825), I suggest to you the employment of another broker than myself (1848), …and in acting for you I often appeared rather as a ship-broker, than as a member of Parliament. (1847), and he also sells by auction; his chief occupation is the latter,—is he not therefore rather a broker than a dealer? (1850), It is better that the tax should be upon the broker than upon the farmer. (1914), Purchasers of commercial paper will usually do better to buy through a reliable broker than direct, as many losses have been caused by companies… (1917) "The merchant can often obtain more funds through the note broker than he could obtain from his local bank." (1922), "Is it not possible to get & [?] better price from one unlisted broker than another?" (1926)
The first instance that comes closest to the comparative form is dated 1937
And some of us broker than others, and yours truly is about the best broker in town.
However, the meaning of broker in the phrase: “some of us broker than others” is still a NOUN.
If broker, as lly's answer suggests, has always been the preferred comparative of broke there should be some evidence of its usage in the Ngram chart. Unfortunately, I discovered none.
Digging further, all the instances of broker than recorded by Ngram refer to the noun meaning. The only exception was the following, dated 1996, a book entitled More Texas Sayings Than You Can Shake a Stick At. However, it is important to note that the jocular form broker refers the VERB break, not to its financial meaning: 1. “Broker than the Ten Commandments” (= to be more broken than the ten commandments) and 2. “Broker than a stick horse” (= more broken than…)
This is not to say that native speakers never say "broker than", but Google Books was created to index the books’ content and analyze the connections between them, determining any given book’s relevance and usefulness by tracking the number and quality of citations from other books. [emphasis mine]
So one is forced to look to Google, and indeed I found some evidence, the catchphrase (or idiom) broker than broke
He thought of her, and he felt honest regret about the whore he had known earlier, missing his wife. "I was broke, broker than broke, and I was powerfully tired, and in desperation, hungry and worn,... (1977)
Now, let's talk about Nigeria for a while." He addressed himself more to me than to the audience. Your country is broker than broke. Your country owes us, the West, billions. (1986)
That was a huge year compared to where I'd been a couple years before. My perception of my time changed. Two years prior I was broker than broke; I was $65,000 upside ... (2003)
*John is completely broke, which is broker than broke, broker than before. Last Friday, someone, a friend, sort of a friend, a guy John recognized from the neighborhood, offered to buy drinks at the bar if John would drive. John drove.* (2018)
more broke than…
On the other hand, the (written) evidence suggesting that native speakers prefer using this informal construction is well-supported. Searching was more broke than (blue line), and even more broke than (red line) between 1900 and 2005 on Google Ngram proved fruitful.
Parties For Pennies (1942)
You'll find, if you do, that you are even more broke than you dreaded you might be— and, unfortunately, just at a moment when you have no spare pennies to charge up to experience.
From The Rivers are Frozen (1942)
put in a box to be filed, and, well, they said, they'd call her if there was anything; but there was nothing, and at last Leo was more broke than she'd ever been and once she nearly wrote to Uncle Bob for help, but she couldn't quite do that.
From How to be Poor (1945)
“ELL, I have finished my book, read it myself, and made a date to meet some of my intimates, more learned and even more broke than I— at a rendezvous of ours where there is an orchestra whose conductor gives us— my intimates and me—”
The Horizontal Hour (1957)
Derek had asked. "God knows you need analysis more than I." The remark had come at one of Mungo's low points. He was more broke than usual, sick of working, sick of working at working. "The plague of the locusts is on me," he conceded
The results spewed by Google's Ngram need to be always checked, and always carefully but there is strong evidence to suggest that native speakers, in casual speech, will opt for “more broke” as the comparative adjective form of broke.