Can I just say that in Our Man Bashir they made a point of saying they had to erase nearly every bit of data on every computer aboard the station, it's cores, etc down to the very minimal machine code for keeping the life support working just to barely fit 5 patterns.
An entire station running computer technology throughout with that kind of storage having to be emptied nearly 100% to fit their base patterns, not necessarily their conciousness which seemed to exist on the holodeck in some other way.
That is not practical, they couldn't figure out how it even happened or worked to even try repeat it and on a starship would have been disasterous as there would have been nowhere near enough storage or possibly power.
So obvioulsy whatever way transporters normally work, they do not store anywhere near as much information on each individual, otherwise the mass transporter evacuations we've seen would be impossible.
DS9 is not a state of the art Starbase like what usually resides in UFP territory. DS9 was a ore processing plant before getting renovated. I doubt they needed that much computing power for everything in the facility.
Voyager on the other hand was able to expand their transporter buffer capacity to beam over the entire crew of a Klingon Starship of over a 100 people in a few seconds.
So I think it's more a limitation of computing power, computing memory, and pattern buffer storage capacity.