This passage, and this style of communication in general, is an excellent instance of a symptom of the author's failing cognitive abilities. Nowadays it would be labeled MCI, mild cognitive impairment, a symptomatic precursor to many kinds of dementia.
The passage is not agrammatical, but it follows such a tortured garden path that its recreation could be a plan for a large estate garden, and, in this guise, a distinctly English one, with none of the strict classicism exhibited in the continental.
For the highlighted passage can be simplified considerably to show its structure:
... This, she fully believed, had the usual share, had even more than the usual share of all such solicitudes and suspense been theirs, without reference...
is structurally similar to:
This ... had the usual share, even if more than the usual share had been theirs.
The convoluted subordination along with false parallelism and improbable contradistinction, starting a new sentence without bothering to start, are really a sign that she was internally, in her own personal writer's monologue, attempting to sidestep the loss of vocabulary for the terms she was trying to explain in this long winded, seemingly thought filled circumlocution.
This particular kind of anomia, and despite its erudition it can certainly be labeled as such, is characteristic of only a few dementias. Some, like Alzheimer's, lead to a loss of expressibility, periphrastic by shorter sentences, more Anglo-Saxon, uninflected verbs. If they are only passing my house now, the children walking to school are going to be late. Others seem to result in a loss of a few items but keep enough faculties to compensate, and may even lose inhibition, leading to longer and longer sentences attempting to capture the finer and finer, even up to exact, nuances of the lost lexemes. Austen has very successfully compensated for her imminent demise by a common tactic subconsciously used by many to cover up difficulties in production of vocabulary, both periphrasticism of the prolix indirect kind, and parataxis of the run-on, articulate but inarticulated kind.
Austen had shown herself to be a strangely popular prose esthetician in her earlier works like 'Sense and Sensibility' and 'Pride and Prejudice' (note the lack of innovation in titling, even 'The Fast and the Furious' people do something). She could keep a train of thought from one sentence barely to the next. But by the time she was writing 'Emma', the predecessor to 'Persuasion', the side effects of her other than most upright of daily habits were taking their cognitive toll; she could barely keep a consistent idea within a single paragraph long sentence. From diaries and correspondences, it is well-documented that repetitive microtraumas from pugilism, severally multiple Oxford commas (a common nearby travel destination for inhabitants of Bath, Austen's primry residence), the fowl malarial miasma of the stables during contests intergalline or canine/murine, and some other third thing contributed to her inability to rationally this is all, as the clinicians of our age are prone to utter defensively, the most not inconsistent with Vascular Dementia:
... They tend to have better free recall and fewer recall intrusions when compared with patients with Alzheimer's disease. In the more severely affected patients, or patients affected by infarcts in Wernicke's or Broca's areas, specific problems with speaking called dysarthrias and aphasias may be present.
Even in her materially privileged lower upper-middle class, without the benefit of contemporary medical practices, the ravages of daily behavior daily stole her words.