"I think we are entitled to own one property that isn't subject to CGT, "
It's a bit more complicated than that. Normally, you need to work out how long you lived there and how long you rented it out as a percentage. You will still need to pay CGT if you have rented your house out.
However, your situation is likely different with you being in the military.
There is an example on the gov.uk site here:
Example
You make a gain of £120,000 when you sell your home, which you owned for 15 years. You lived in the whole property for 7.5 years, then you let it out for 7.5 years.
You get Private Residence Relief for the time you lived there (7.5 years). You also get relief for the last 9 months you owned the property, even though you were not living in it.
This means you get Private Residence Relief for 8.25 of the years (55% of the time) you owned the property.
You get Private Residence Relief on the same proportion (55%) of your gain. This means you will not pay tax on £66,000 of the gain.
The remaining 45% (£54,000) of the gain not covered by Private Residence Relief is your chargeable gain.
https://www.gov.uk/tax-sell-home/let-out-part-of-home
However, it may not be quite so bad in your case as there are also extra reliefs available if you had to live away from home in the UK for work or for any period when you were working outside of the UK.
From your OP I guess that you have been overseas for a fair bit of time.
The rules on CGT relief can get very complicated and it really would be best to speak to an accountant who understands this and also the position with you being out of the country and, for at least some of the time, having more than one property.
https://www.gov.uk/tax-sell-home/absence-from-home
"buying a "second property", causes a prohibitive leap in stamp duty."
With the extra stamp duty, that is only payable if you have more than one home. If you then reduce the number of homes you own to just one within three years then you can claim a refund of the extra stamp duty that you paid.
But, if it takes more than three years to sell the extra houses then you do not get any refund.
It's probably easiest to sell all of the properties first in your situation before buying a home.