I also understand that sulfur cell inclusions are usually elemental sulfur wrapped up in PHA (poly-beta-hydroxy alkanoates) polymer.
This is not correct! It is true that most PHA producers generally belong to the Gram-negative group of bacteria. However, PHA is not used to store sulfur. PHA is there to store excess carbon and energy. Though, this energy can come from sulfur metabolism!
From Brock Biology of Microorganisms 14h edition I cite:
"The oxidation of sulfide is linked to the need for electrons to drive either reaction of energy metabolism (chemolithotrophy) or CO2 fixation (autotrophy). In either case, elemental sulfur from the oxidation of sulfide may accumulate in the cell in microscopically visible granules [...] Interestingly, although sulfur globules appear to reside in the cytoplasm, they are actually
present in the periplasm [...]"
"Why would it be impossible for Gram-positive bacteria to store sulfur
as gram-negative sulfur-oxidizing chemolithotrophs can?"
The as here is very important. Because some Gram-positive bacteria are perfectly capable of storing sulfur but not in the same way as Gram-negative bacteria. As we know, in Gram-positive bacteria the periplasmic space is found between the inner membrane and the peptidoglycan layer which – I assume so – is not suited to "hold" or produce these granules in a similar fashion.
To give a bit more context:
Sulfur oxidation and sulfur reduction are two different processes that involve the transformation of sulfur compounds. Certain Gram-negative as well as Gram-positive bacteria (e.g. Desulfotomaculum) are able to do so. Some strains are even able to do both reduction and oxidation! In either case, for both types of bacteria, there are strains with sulfur metabolism involving the storage and usage of sulfur for energy production, just in different manners.