I'm glad I came across your post, Ken, as it started me digging (what else to do whilst we're in the slammer?) and I came up with some info on the BSA A7 / A10 net which gave me a bit of a jolt (links below).
I have a book of data for BSA models, which BSA published in 1955. Tyres used on the A.10 Golden Flash were 3.25x19 front, and 3.50x19 rear - and Speedmasters on front and Safety Mileage on the back would have been typical fitments.
But this is how the tyre pressure recommandations have changed over the years . . .
From BSA, 1955 - Front, 17psi; Rear, 19psi.
From Haynes Manual (maybe 1980s?) - Front, 18psi; Rear, 20psi.
From Lightning Spares in 2009 - Front, 28psi
, Rear 30psi
, two up!
Brian, of Lightning Spares, told the OP on the BSA forum that he'd lost count of the number of soft tyres he's seen at BSA meets only to be told by proud owner they are running at BSA handbook stated pressures.
The problem arises because the 'cling' rubber which came in around 1963 - and which has been dramatically improved since then - is much softer than pre-cling rubber, which means if you run at the original recommended pressures, the side walls flex far too much, and - as the OP on the A7/A10 net found - you can rip the valve right out of the tube due to the tyre slipping on the rim! Luckily, he was only doing about 30mph at the time, so he got no more than a nasty fright.
I think your best bet is to contact a tyre specialist, tell him what tyre size you're using, the weight of the bike, and the sort of load it will be carrying. Arthur Gent's book quotes a dry weight of 280lb for a Cruiser 39, so you should be able to check the weight, one wheel at a time, on a set of bathroom scales.
HTH, and best regards,