The seat mounting rail is important as it provides the back and centre mounting for the rear mudguard mounting AS WELL AS being the thing the seat brackets bolt onto!
Near the back of the frame, at the top, there should be two cross pieces which I sincerely hope ARE still intact. The front of the seat rail merely hooks onto these, it is then held in place by two slotted lugs that just drop down onto the top bolts for the rear shock absorbers inside the frame.
Have a look at this one: it's slightly different (used on the '58 Constellation and the Fury models) as it loops round the back of the mudguard and is used with 5" mudguards. The Bullet version is open at the back and uses another couple of brackets to bolt onto wider mudguards, but the principle is the same.
The front of the rear mudguard his held on by a bridge that bolts to another tow small lugs welded to the frame. You can see how it fits from this picture of a Fury model (picture lifted from the internet, apologies, can't remember where!). I suspect those lugs are still there, holding the battery/air filter box onto the frame.
Going back to the first picture you can see the mounting point drilled for the front seat bracket, there's another one the other side. The rear set mounting is via single bracket in the centre which bolts onto the loop in the middle of the seat rail (which also forms the centre mount for the mudguard).
Hope this makes the factory set-up a bit clearer. You can use any system you want, but this one looks best, I reckon.
A.