It is far simpler to order a selected design and modify it that it is to select an all new design. Changing the propulsion Turbine from LM2500 to MT30 would be actually a fairly low risk change. Being an Electric pod propulsion, changing to the lower maintenance, more efficient MT30 on a 1:1 basis is fairly straight forward. The MT30 was repackaged to assist with this this change and the LHD has quite large mechanical spaces. You would get more power output, lower maintenance and operational costs, greater range, common turbine across the new generation of RAN ships. Again there is nothing wrong with the lm2500, it wouldn't have to be changed, other than it would likely be changed anyway during a mid life refit. The LM2500 used on the LHD isn't a marine engine variety anyway and the LM2500 used on the AWD is a much older version too so there isn't a whole lot of commonality at the current space in time. The MT30 really doesn't require anything other than observation and fuel during deployment it is extremely low maintenance which is why nearly every navy is transitioning from the good old lm2500. IMO replacing the lm2500 with an engine of a different type in our existing LHD's will probably happen over their life anyway.
As for speed Cavour with its 4 Lm2500 requires 25 tons of fuel per hour at full speed, so with that fuel usage you would have to resupply something with JC1 fuel reserves (1,600t) every 48 hrs, you get 2 days range at full speed. So range and endurance is very short at full speed. Sure you can put more fuel on, but then you have less space and weight for your mission. I expect most ships to cruise around at ~20kts unless there is some specific reason to go fast. Ditching poded electric propulsion would result in less room in your ship as well.
Japan has a specific problem because of the proliferation of diesel electric subs, ships and planes in their region. They don't need long endurance, they need speed. Particularly as a ASW unit, in that area of operation. Japan sees speed as an essential component of their fleet. The RAN doesn't have that problem. 22-24kt will be fine.
JC1 current aircraft carrier format.
A 20 meter lengthened LHD would give you 2+ more jets/helos on the deck, another helo landing spot, a longer landing (for rolling landings) and take off (heavy loads). 4 more helo/Jets in the hanger, a larger lower deck more more vehicles, more space, more room, more stores, more embarked forces. This would bring it closer to the aviation capabilities of a more dedicated platform, but with still the flexibility of the LHD. You would also be within spitting distance to the size of a Wasp or America class, same width, nearly same length, but with a ski jump. And with the familiarity of 3 of a type, also designed to operate along our new AOR and AWD's. With our current LHD operating costs.
I think that level would be pretty significant.
USS Bataan LHD-5 and USS Bonhomme Richard LHD-6 - Each with 15 harriers on deck and ready to launch. So an extended JC1 or Italian aircraft carrier Trieste, would get you to that level of capability.
So does the RAN just want a bigger and more capable ship able to deliver amphibious and aviation capability, or get an additional dedicated aviation ship (with crewing/money from magic land) and make do with its current limitations in amphibious capability.