Your coating of whiting is very thin IMO. I put it on and build it up quite thick.
I mix the powder with plain alcohol instead of acetone.
It allows the slurry to set on and maybe in the wood a bit before setting up from the evaporation of the alcohol. The acetone evaporates so quickly.
The often stated reason for using acetone to further disolve oil and bring it to the surface for the whiting to absorb just doesn't make much sense to me. The acetone in the whiting slurry mix is evaporated away in a matter of a few seconds after it hits the surface.
The shell of whiting sits on the wood for days.

The whiting powder shell is quite delicate and brittle, just the nature of the stuff.

If it's not turning color,,brown, yellow or anything from it's bright white,,then it's not absorbing anything from the wood plain and simple.

If there is oil still in there it will draw and absorb it from the surface.
It is a terribly slow process but a good one. Not so good in this day and age of I want it done Now.

In between coats there is no need to rinse the whiting from the surface of the wood.
Just brush the coating off. Often you have to pick some of it out of crevices like screw countersink and deep inlet edges. Go easy so as not to damage the wood.
I use one of the Military M16 cleaning brushes. Stouter than a plain toothbrush, though that'll work OK too. The stronger M16 brush will clear more out of the grain and still not damage anything.
Air gun will clear a lot of it AFTER the initial brushing. The dust is a killer, so take precautions.
Not something to do in an enclosed area.

Recoat and rehang. Leave it and forget about it. Check back and recoat if it needs it in any areas anytime.

When you think you're done with the Whiting,,then do the rinse.
Any brushing with a rinse use a soft brush like a paint brush. Wet wood damages easily.

After the rinse and with the wood still wet I use wood bleach (Oxalic Acid),,NOT Laundry Bleach (Sodium Hypochlorite).
1 Tbs/ qt of water. Warm it in the MickeyWave for 30 to 45 seconds. Dunk or paint this on the wet wood. Slosh it on.
It'll even up the color and lighten it at the same time. It'll remove any discolorations in the wood from old distress marks and the like.
When it's to your liking,,rinse completely again,,cool water this time. Taking care again not to damage or bruise the wood. It'll be very easy to damage.

Now hang it and let it dry on it's own. Don't be tempted to force dry it w/a torch or even placing it in a hot box or on the dashboard of the family transporter.

It won't take more than a few hours to appear completely dry,,sometimes less.
I leave them for a couple days before starting finishing.
The wood will take stain and finish beautifully.

I do use a lacquer thinner soak at first to remove some stocks with heavy oil in them.
I never completely trust them to do the entire job as there is really nothing to absorb the oil once it's in solution in the thinner wether it's acetone or lac/thinner, or whatever.

That's where the whiting powder or the hotbox with the absorbent like cat litter comes into play.