For the Space Shuttle, the local acceleration due to gravity was calculated onboard based on the vehicle position. So, as you say, they kinda did "carry a 'Gravitational Ephemeris'”

> Because the vehicle's location changes with respect to the Earth as it
> orbits, the state vector is constantly changing, and nav is
> continually having to recompute it. This is done in the General
> Purpose Computers (GPCs) via an algorithm known as “super-g
> navigation.” The Super-g Algorithm performs the following functions:
>
> a. Given the state vector and gravitational acceleration from the last
> cycle, a new position vector is estimated using either modeled drag
> acceleration or IMU-sensed acceleration. 
>
> b. The gravity at the new position is calculated. 
>
>c. Using the change in gravity from the past
> to the current cycle, the position and velocity vectors are
> recomputed.

From [Guidance and Control / Insertion, Orbit, Deorbit Training Manual][1] paragraph 2.3

More information about the gravity model is available in the [FDO On-orbit Console Handbook][2] paragraph 3.5.1.1

> The Orbiter's gravity potential model utilizes an infinite series
> expansion of Legendre polynomials called Pines method. This recursive
> algorithm accesses a database of harmonic coefficients arranged in
> lower-triangular-matrix form. An element of the database is termed
> Jn,m, where the row n is the harmonic's degree and the column m is its
> order. When m=0, the coefficient's effect is symmetric about a
> parallel of latitude, and it's termed a zonal harmonic. When n = m for
> a matrix diagonal coefficient, its influence is symmetric about a
> great circle of longitude, and it’s termed a sectorial harmonic. No
> latitude or longitude symmetry is associated with the action of
> coefficients having n ≠ m, and they are termed tesseral harmonics. The
> onboard model is configured with a Goddard Earth Model 9 (GEM9)
> database truncated to fourth degree and order.


  [1]: https://www.ibiblio.org/apollo/Shuttle/Crew%20Training/G_C%20Insertion%20Orbit%20Deorbit%20Workbook.pdf
  [2]: https://www.ibiblio.org/apollo/Shuttle/MCC/FDO%20Console%20Handbook%20-%20On-orbit.pdf