The tritone substitution concept does not always include only dominant 7th chords. The most obvious choice of chords (using tritone substitution) for A7 and D7 would be Eb7 (instead of A7) and Ab7 (instead of D7). However, you can always try other chord qualities as well, such as maj7 chords in this case. The original progression is just G7 going back home to C. I added a D7 (dominant V chord of G7) before the G7, and an A7 (dominant V chord of D) before the D7.
Instead of keeping it that way, I then used the tritone sub on the A7 and D7, finding the chords Ebmaj7 and Abmaj7.
Original progression: G7 ---> C...
New progression: Ebmaj7 ---> Abmaj7 ---> G7 ---> C...

Now, you could look at this progression from another angle too;
The Ebmaj7, Abmaj7 and G7 chords can be found in the key of C minor. So you might analyze this as borrowed chords from the C minor tonality, rather than C major.

Hope this helps!
Kind regards/Emil

Really enjoyed the lesson. I have question about tritone substitution.

Most of the theory that I've read on this subject says that a dominant 7 chord can be replaced with another dominant 7 chord which is a tritone interval away from the original. However, in the Amazing Grace arrangement, you replace an D7 and and A7 with an Abmaj7(#11) and an Ebmaj7.

They sound great but I was just wondering if there is a rule that the new chord substituted for the dominant 7 should also be a dominant 7. In other words, when can the new chord be something other than a dominant 7?

Hope that makes sense.

Thanks,
EB