Sounds like the integrated amp uses the 12AX7s the same way as in the model 400, less the three tubes in the FM multiplexer circuit.
Two are used in the phono stage, so unless you plan to spin records, these can be any working 12AX7. On the 400, these two 12AX7 tubes have tube shields, whereas the others do not.
The remaining four 12AX7s are used for:
Voltage amplfier
Tone control amplifier
Left channel driver/inverter
Right channel driver inverter
This is where it gets to be fun. You can try changing these tubes until you find some you think enhance the sound. For myself, I have tried the smooth-plate Telefunkens, and some GE made in USA. Both are nice, with the GE being somewhat better focused that the Teles, in my opinion. (I actually like the GEs better in this application than the highly revered smooth plates.)
The tube that will blow you away is the Raytheon 5751 with the windmill shaped getter. There were several types, some with double mica insulators and with or without support rods. If you can try to get any of these for your Fisher and you won't be disappointed.
Also, there is a Sylvania 5751 that is supposed to be fantastic, but very expensive and hard to get. If you have trouble finding the more desirable 5751s, try some of the better received JAN 5751s, as these frequently show up on eBay. The JAN tubes were mil-spec tubes, so they are rugged and have low microphonics, or they would not pass quality checks for these government tube supplier contracts.
If you go to audio asylum - tube asylum, you can read some interesting reviews of both 12AX7s and 5751s.
5751s probably won't work well in the phono section because the gain is only 70% of that of a 12AX7.
Please let us know what you find pleasing.