SLBM Booster Tests for an Aussie "Baby Boomer" SSBN?

In mid 2022 in the dual-use tradition of the US Atlas missile, US NASA is working with Australia to launch (see video here and above) sizable rockets in Australia. This is first time NASA has done this outside the US and it follows the AUKUS agreement. Whether this is connected to future manoeuvrable hypersonic MIRVs, only time will tell.

To get an idea of the size of these rockets see the NASA employees here and below working on a rocket in Australia. Photo taken July 2022.

Some broad-brush thoughts: 

Block V Virginias and I suspect future UK SSN(R)s (aka Astute Successors) available in the 2040s will boast around 4 VPMs. 

The current Astutes have a beam/diameter of 11.3m (which increased by 1.5m from the preceding Trafalgars). This suggests the SSN(R)s may have a diameter of
11.3 + 1.5 = 12.8m.

Where I'm going is that a 12.8m diameter should allow a missile 12m tall. Even a Trident I C4 Missile was only 10.2m tall. It sported 8 MIRVs with a range of 7,400km https://en.wikipedia.org/wiki/UGM-96_Trident_I . 

Adding 2m, with lighter booster casings and more energy/kg propellant should permit a Trident I* range around 10,000km. 

A SECOND THOUGHT 

Australia's intention to build 8 or more (10?) SSNs could be rationalised to 6 SSNs protecting 4 full sized SSBNs. These SSBNs could sport full sized Trident IIs D5 (or D6 or D7 by the 2040s) of around 13.58m tall https://en.wikipedia.org/wiki/UGM-133_Trident_II . 

With some pushing by the US and UK
the good burghers at the IAEA
will happily add Australia to the legal nuclear “haves” list. https://en.wikipedia.org/wiki/Treaty_on_the_Non-Proliferation_of_Nuclear_Weapons#Criticism_and_responses

Simple? Elegant? What could go wrong?! :)