Yes, everything has to compile in PROGMEM. The sketch can't put values into flash. Note that there are only pgm_read_xxxx instructions, no pgm_write.
More, the pgm_read_xxxx instructions are only for the basic data types. But hey, isn't all the data you are using the same type?
What I would do is make 1 of each class object as a buffer for each and load data into the buffer as needed rather than have them all loaded when I can only work with 1 at a time anyway.
Regardless of how you do it, that's what you have to work with if you want to use the relatively huge storage space in flash. Even if you were to put the data on an SD card (slower but gigs of space instead of kilobytes), it'd still make sense to work through a buffer.
OTOH you can get an Arduino or compatible with more RAM like a Mega2560 or Teensy++ or I think Crossroads has a design that uses a ATmega1284. All of those can use external RAM directly addressed by the MCU. I think it is Rugged Circuits that has up to 512k for the Mega2560 though that is in 64k banks you switch between. You could put a lot of sky up quicker that way.
Another sort of solution is to use a tablet/netbook/laptop/PC USB-connected to your Arduino as your data source. The Teensy's and I think the Leonardo do full speed USB as opposed to 115k serial to and from a USB chip (read: bottleneck) used by the UNO and Mega2560. LOL, a PC connected solution can support multiple Arduino-type machines through USB hub which would let you scale up for speed as each can probably draw some number of stars faster than human eyes can follow.
And that leaves me wondering how you place star-dots on the dome? I haven't been in a planetarium in over 40 years, the technology has probably changed just a bit.