Lancaster, as you should know, both 7x53R and 7x54 has been designed for hunting big forest birds. After WWII finnish moose was very rare animal so shooting these birds was the easiest way to hunt for food.
At war time 1941-42 SAKO developed their 7x33. It´s donor case is 9x19 Pb. This kaliber is good for bird hunting with dog but only for quite short distances so VPT (Finnish goverment ammo factory) developed two calibers for longer distances. This happened just after war time so the easiest available donor cases were 7,62x53R and 6,5x55. Light 7 mm bullets by SAKO were too very well available so 7x53R and 7x54 were quite locical solutions. At that time 7,62x53R was banned for any hunting purposes.
Later SAKO developed 10,1g half jacket bullet for those who wanted to hunt moose with bespoke caliber rifles. But on year 1969 new law banned these calibers for that use.