The 'problem' A10 barrels are the standard 'square-fin' ones when used with an engine tuned to Road Rocket/Super Rocket etc spec - the higher-tuned engines needed more meat around the barrel base, hence the 'thick-flange' barrels.
The standard barrels don't seem to have any problems coping with the later Gold Flash spec (7.25:1 'flat top' pistons and 356 cam) even when sleeved. I'd reckon there's a good chance your barrels will be fine.
That later Gold Flash spec is also the Ariel 'export' and 'sports' spec; the Cyclone spec had the higher 8:1 compression ratio, with standard barrels, and I don't think these have an issue with barrels splitting either. However, if you're going to go above 7.25:1 and the 356 cam you might be advised to use the later big-bearing crank and rods but that won't fit straight into early crankcases....
I've got a link somewhere to a discussion in a BSA forum about the problems sleeving the BSA 'thick flange' barrels - bear in mind that some people are using very high states of tune with these. The more successful 'fix' was to braze the sleeves in the barrels at the top and bottom - similar to what Nev is describing with welding, but it might be easier.
'55 Huntmaster, '56 VH, ' 51 VH, '80 R100RT, '00 Sprint ST (but all those Ariel parts can only make one running bike...)