As mentioned by the OP in a comment, the answer may be found in the article Sherwood Cummings, "Mark Twain's Moveable Farm and the Evasion", American Literature 63(3) (1991), pp. 440-458, which may be found on Jstor. There's actually much more to this issue than that one line from Aunt Polly. Allow me to answer by challenging one assumption made in the OP which is actually incorrect, and by subverting the question to a different but related one, namely:
Where is the Phelps farm?
I know the Phelps' farm is supposed to be in Arkansas ...
Nope! In fact, there has been a lot of disagreement among Twain critics about exactly where it is. Quoting from Cummings's article (p. 1):
Located where Huck and Jim's long raft voyage down the Mississippi ended, the Phelps place must be considerably south of its Missouri counterpart, but just how far south is a matter of disagreement. There are scholars who put it in Arkansas and others who put it in Mississippi or Louisiana. It is the purpose of this study to sketch the history of that disagreement, to offer a precise location for the farm based on fresh analysis and evidence, and, more importantly, to suggest how the disagreement is a consequence of Mark Twain's own ambivalence.
The following paragraph (pp. 1-2) details the writings of many Twain scholars who variously determined the Phelps farm to be in assorted parts of the states of Arkansas, Louisiana, or Mississippi. Strong evidence for Arkansas is Twain's own assertion, in his autobiography, that:
In Huck Finn and in Tom Sawyer, Detective, I moved it [the farm where Twain himself spent his childhood] down to Arkansas
In Tom Sawyer, Detective, the farm is clearly stated to be in Arkansas. But this was written over a decade after Huckleberry Finn, and several Twain scholars have determined from textual evidence in Huckleberry Finn (including the "eleven hundred mile" which you're asking about) that the farm wasn't written to be in Arkansas at all. After summarising the existing body of literature on this topic, Cummings summarises his own research as follows:
It was my curiosity about such questions that led me to search out old maps and records and to learn something about lumber rafting. My inquiry has satisfied me that Mark Twain located Pikesville on the site of the now vanished village of Point Coupee, Louisiana, on the west bank of the Mississippi, thirty-seven river miles north of Baton Rouge, across and somewhat upstream from St. Francisville.
Point Coupee Parish still exists and you can find it on Google Maps. It's in Louisiana.
Cummings spends several pages justifying in considerable detail, using evidence from the novel and knowledge of contemporary geography, his claim that Pikesville equates to Point Coupee. In this answer I'll mention only what I found the most clinching piece of evidence (p. 7):
Point Coupee, then, seemed a likely Pikesville, but was there corroborative evidence? Speculating that Mark Twain might have used the government map that he had previously acquired for his Mississippi River trip as a present aid in developing the locale of Pikesville and the Phelps farm, I sent for a copy. Drawn to a scale of one inch to one mile and consisting of thirty-two panels, each twelve by twenty-two inches, Major Charles R. Suter's 1878 Map of the Reconnaissance of the Misssissippi River shows considerable detail. From evidence in Huckleberry Finn we know that the Phelps farm is four miles below Pikesville on the river road, that on the side away from the river there are cotton fields and beyond them woods, that in the opposite direction there is a narrow strip of "bush," then the river, and out in the river a "woody island." Four miles below Point Coupee on the Suter map is the cleared land of the riverside Preston plantation, woods a mile to the southwest, and to the northeast, in midriver, a wooded island.
How's that for confirmatory evidence?! Cummings also speculates on where the name "Pikesville" came from, providing even more confirmation for his theorised equivalence (pp. 7-8):
The particular copy of the Suter map I studied provided an unexpected bonus: the original, which is part of the Walter Havighurst Special Collections, Miami University Libraries, Oxford, Ohio, was once owned by Samuel Fulton Covington (1837-1889), an incorporator and later president of the Globe Insurance Company of Cincinnati. Covington's special interest in river-traffic safety prompred him to pinpoint on his map the locations of steamboat accidents. At Point Coupee he wrote, "GEN. PIKE, BURNED." Further search on my part identified the General Pike as a 308-ton sidewheeler destroyed by fire at Point Coupee on 18 April 1849 with the loss of one life, facts that Mark Twain may well have been aware of and which may have given him the name for Pikesville or "Pikeville" as its first appearance in the holograph would have it.
So how about that 1100 miles?
Coming back to the original question ... Cummings also confirms that his proposed location is consistent with the "eleven hundred mile" from the text (p. 7):
In the river-mileage figures plentifully printed midstream on the Suter map there is further corroboration. Suter's river mileage from Greenville to Point Coupee, in comparison to our estimate of 350 miles of raft travel from Wilks-town to Pikesville, is 349 miles. From the confluence of the Ohio River to Point Coupee, Suter's mileage is 850. Add to that the slightly more than 300 miles from Hannibal to the mouth of the Ohio, and Aunt Polly's traipsing "all the way down the river, eleven hundred mile" (p. 358) makes sense.
So to answer your question of "how is it 1100 miles from Hannibal to southern Arkansas" - it isn't. If you reach a contradiction, alter the initial assumptions :-) No geometries were harmed in the making of this novel.
