I'm building an Intimidator 3". The booster tube is 44" long and not wide enough for me to reach down to the top of the motor mount and the shock cord mount eye.
Indeed.
You really need 4+" airframes, ideally 5+", to be able to work inside the tube with an adult hand.
If you have access to captive child labor resources, THEN you might be able to go smaller.
I'm sure it would be perfectly fine for me to attach the cord and never need to replace it (?) but those types of things bother me... I'm always trying to make things easy to repair or replace.
True on the first count - the only time I EVER had to replace a shock cord on a HP rocket, was due to a FWD closure failure and the resulting fire inside the airframe.
The repairs included replacing the compromised MMT tube, so gluing a new shock cord to the tube wasn't that much more of a hassle.
See my "high fidelity" sharpie sketch

attached... I would tie a quick link into the cord about 6 feet from the end, run the end through the mount eye, and attach it into the quick link - so a 'doubled' cord inside the booster, but able to remove/replace it if necessary.
Any reason this is a bad idea?
It works if space allows, but on a 3" airframe, it is likely too tight.
To be usable, you really need 1+" of buffer space between the inside and outside diameters of the FWD CR. More than 2" would be better. Then, you place the eye in middle of the CR, and still have some room to thread the shock cord into the eye and pull it out without airframe interior wall getting in the way.
So on a 3" airframe, figure 3-(~1"*2) == max ~1" motor mount diameter, or max 24" MMT. That would obviously be way too puny for the 3" Intimidator, that comes with a 54mm (2.126") MMT.
Other than access constraints, it would work.
HTH,
a