In most inventory database applications, the unit and quantity are two
different fields.  The best approach would be your first, which would be to
split it into two fields.

I think your problem may be that since you have 3 million records, you might
be bumping up against the access size limit of 2GB.  This means it  would be
best if you can do it with a couple of update queries. Other than that, the
process is pretty straight forward.

First you would need to modify your table design to create the new field.  I
would make the new field numeric to hold the quantity because the existing
field is text.

Then in the update query, you could update the new Qty field to:

Val([OldField)

To use your example: 311 ea would return 311
The old field will still contain 311 ea
The new field will now be a numeric 311

Then run a second query that would take the quantity off and leave only the
unit.  This formula assumes there will always be a space between the number
and the unit.
Here is a formula for the update value:
right(trim(x),len(trim(x))-instr(trim(x)," "))
the original field will now contain
ea