The 37 x 303 Davy Crockett has a rim of 50.5mm. I can't see how that would be made from a Bofors case as the thickness on the inside is much thicker to facilitate the method of firing. The start of the neck on the DC starts at 80mm and ends at 93mm (measured with a ruler so a bit rough).
The nearest I can find is the 37 x 202 Vigilante that has a rim of 55.6mm and cartridge length of 219mm (much shorter than yours). The shoulder starts at 150mm and ends at 185m (roughly). The Vigilante was based on the bofors, see:
http://www.quarry.nildram.co.uk/RED QUEEN.htm
Bofors did do a 37 x 320 round, the M/39 with a rim of 56.1mm, could it be one of these? It would match the length of your case but the shoulder height you quote is much lower than on the M/39
I've attached a few photos of verious Bofors rounds, the 3 on the left are Bofors L70 plus various necked down version, the 4th from left is Vigilante 37 x 219, next is a Bofors L60 and the 20mm version next to it with the Davy Crockett on the right. Perhaps its like one of these?
The second photo shows the bases of the Vigilante, Bofors L70, bofors L60 and Davy Crockett for comparison.
A photo of your mystery round would be good, if you pm me your e mail address I can post the photo for you.
All rounds shown are INERT.
Dave.