The debate over what was actually put down on the recording could go on forever and it wouldn't surprise me if The Beatles and George Martin forgot what was involved, not too long after the event.
However, there are a number of clips on You Tube of The Beatles playing this song live and it can clearly be seen that both Lennon and Harrison are holding down an F major chord with an added 9th on the top E string, that is, 103213. What makes this chord sound right is McCartney playing a D bass note (open D or D on 5th fret of A string). That D bass note also helps you pitch correctly when starting the vocals.
That's how we cover it in my band using a 360/12, Strat and 4001.
Having said all that I agree the best compromise when playing it on a single guitar is G7sus4 or 353533. You've got to have that D in there somewhere.

With two guitars, it sounds nice with 3x0213 and xx3213 with a bass doing a high D. This is perfect for a band without a keyboard. May not be right, but sounds nice and full!

I also play it as a G7sus with 353533. But remember -- the chord was recorded as guitars and pianos together with stacked chords of different kinds, so that what we're doing here is merely a condensation to enable covering it on stage or for personal enjoyment, albeit those are two very good reasons indeed.

But it is without a doubt the great opening jangle. After all these decades, our ears are dulled to how exciting that must have sounded when it first came out and that chord along with the opening of the movie just hit everybody out of nowhere.

I've always thought that, however a person does play it, to learn that chord and play it cleanly should be an elemental rite of passage for anybody aspiring to own a Rick 12.

From wikipedia:

"Analysis of the chord has been the subject of considerable debate,[15] with it being described as G7add9sus4,[16] G7sus4,[17][18] or G11sus4[12] and others below.

The exact chord is an Fadd9 confirmed by Harrison during an online chat on 15 February 2001:[19]
Q: Mr Harrison, what is the opening chord you used for "A Hard Day's Night"?
A: It is F with a G on top, but you'll have to ask Paul about the bass note to get the proper story."

That would make sense, as the closing chord is the same thing arpeggiated alternately with and without the add9. The Fadd9 also introduces an A note into the mix, and so makes the mystery continues.

George claimed it was an F with an added G note. I would assume he knew what he played! You have to figure in George Martins piano chord.