The best subwoofer for any LS3/5A is none.
The tuned-in bass hump is one complicating factor. The other is the B110's (or equivalent in newer form) transient speed. Not even an REL sounds fast enough to keep up. Subwoofers are mostly poor dynamic mismatches to small speakers anyway. They are particularly compromising of everything about the LS3/5a that attracted you in the first place.
If you absolutely must sub-optimize them with a sub, find a Zu Mini-Method or Zu Method. It's fast enough to put you in the realm of not being distracting.
The better way to get a bit deeper (and better) bass from the LS3/5a is to take inspiration from the '70s Double Advent System: add a second pair of LS3/5A, stack then inverted so you are running top to bottom, w-t-t-w. On stands. They'll image a bit better if you make spacing blocks the height of an old 35mm film canister to put between the speakers in each stack.
Several great things happen: 1/ At a given volume each driver is less strained. The little BBC speaker begins dynamic compression later in a rising SPL curve. 2/ The mid-bass hump sounds flattened a bit at same volume as with a single pair. 3/ You get impedance flexibility -- wire in series for 30ohms if you run OTL tubes, or 7-1/2 ohms in parallel if your amp lacks 16ohm outputs. 4/ You will hear mild bass extension. 5/ Image scale improves on large music sound staging. 6/ All aspects of the LS3/5A sound will be present, but more relaxed.
I ran this configuration for many years, both with OTL and TO tube amps. Everything that Absolute Sound observed as gained by doubling Advents was realized doing same with LS3/5A, and for that matter the Double Quad ESL System too.
Get a second pair. No added footprint. Use good stands and BluTak. Surprise yourself, be happy.