The Singapore strategy should have been revised once Japan took FIC in Sept. 1940. That gives a post BoB UK more than a year to sort out a new strategy.
They sort of did - they had a couple of Militia type battalions on hand in early 1940 - by Dec 1941 they had 3 understrength and under equipped Divisions
But due to competing demands on available forces could not send more
I think at minimum they should have left Hong Kong with the minimum troops to make a show of force if attacked and concentrate on holding Malaya once it becomes clear that the Japanese are massing forces in FIC
But there's still the need to hold Rabaul, Ambon, and Timor
As I said before the only strategy I can see were enough troops are available is if the Australian and NZ governments demand the return of their forces from North Africa and the Middle east once the Japanese invade FIC and use the 2nd AIF as the core of Malayas defences.
Britain had 29 Divisions sitting in the UK in various stages of training and tables of equipment (Germany had 100 Divisions plus sat in Europe so you can sort of understand why!) in 1941 so they could with little risk send 4 additional replacement divisions that year to relieve the 3 Australian and 1 NZ divisions allowing them to move east.
This places 5 Divisions (including the NZ Division), plus the 2 Indian Army Divisions which could each be reinforced to a 3 Brigade force by the inclusion of the Hong Kong Brigade and C-Force if still sent.
Maybe Canada would allow 1 of its divisions to serve outside of the UK either in North or East Africa or freeing up Brigades from say Malta or Gib to allow those units to serve in North Africa?
Tanks? I would even send a Brigades worth of Covenanter with the idea that the Australians would use them to train their fledgling Armoured Division and setup a training area in Malaya!
Yes it was a pretty poor tank but the Australian 1st Armoured Brigade would like their British and allied tank units that had the tank inflicted on them become very good at 'tank husbandry' - and a poor tank is better than having no tank and the Japanese tanks were pretty less than ordinary light tanks