All the same cassettes?

Electronic or manual shifting on the TT bike?

TT bike would be on the 53 big ring, mechanical.
Road bike would be on a 52, again mechanical.
The climb is basically all in one gear, except for the flat section which is two cogs down, and then two cogs back up again.
I think I can hols an aero position for the entire climb.

I think that could be a close call. The aerodynamic benefits at 24km/h are relatively low and the impact of 2.5 or 3kg on a 4% gradient while small is not irrelevant. I think the deciding factor might be whether you can produce the same power while climbing on both bikes? And especially whether you'd intend to finish with an out of the saddle effort on the road bike that might be less effective on the tri bike? I think this may be somewhat personal rather than a definite answer one way or the other.

Is it possible to can test both setups prior to the event?

If it was me, and not having the benefit of testing both, I'd lean toward a road bike with clipons and aero wheels.

Another issue is how aggressive your TT bike is setup. If I used that bike, id likely want my hip angle fairly open.

A big factor here also is what bike you feel the most confident with.

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The Giant with the aero wheels.

I did a mountainous century last year with several 5K to 10K long climbs. The toughest was a 700M climb over 10K. I did it on my TT bike with deep wheels, and that was a horrible equipment decision. The geometry was awful for climbing, and I could not effectively get out of the saddle. When I do that one again, it will be on my road bike.

Your TT climb sounds like a perfect match for a standard road bike. I would not worry about the clip-in bars, the odds are you will never benefit from them. And, you will want that area of the bars for sitting upright on the extended, steep sections. If the average grade is 4%, then you will have sections at 10% or greater. Climbing 10% on a TT bike is very difficult.

From his description of the gears used, there is no steeper sections just a continuous low angle hill, TT for sure.
Maybe consider moving the seat a little forward to open out a little for full power.

It was the gearing and speed that caught my eye too, but in the other direction. 25 kmh on a big chainring is very slow for my type of riding. I would usually be on the small chainring at that speed. So, it looks like a very high force, low cadence effort. That is why road bike geometry seemed like the better choice. I can push much greater force in a road bike position than I can in a tri bike position. But, if I am spinning at 90-100 RPM, then both bikes are comparable in power efficiency for me.

In my experience, once I get below around 25 - 30 kph, the benefits of the aero TT position tend to give way to the power efficiency of the road bike position. But, others probably have different thresholds.

I'd run a 42 up front and a tight cluster that put the most used gear in the middle of the cluster.
So for the speeds he suggests, a 12-25 would be ideal.
TT at 83 rpm for me.

Agree completely.
Any aero benefit from the TT is immaterial at such slow speeds. You need to have your power centered aft for the constant climb and you need to push less weight. 2.5kg is significant.

Lastly, you'll look like a tool doing a hill climb TT on a TT bike. It's not a velominati rule but it should be.

Overall I am leaning towards using the road bike and clip ons. I think that I can hold the aero position through the false flat pretty and the steadier sections of the climb pretty well, and use the hoods to get out of the saddle when I lose momentum through corners.
It's a funny climb, and one I have trained on a few times. Whenever I have tried to finesse it with a higher cadence I simply can't get the speed up to the level I can with a higher gear and lower cadence. It's kind of a muscular effort rather than an aerobic one, and usually I do spin rather than grind.
Thanks everyone for your input.