Hello and welcome Peter ! :)
I have had both AII and AIV magnets in my Stormy Mondays - and as Tom has just said, the AII is warmer and sweeter , but perhaps softer in the bass strings than other pickups. They are not muddy, but neither are they notably tight, but just articulate enough to not sound harsh against the relatively sweet sounding top three strings.
I tried an AIV magnet, which made the whole thing more detailed, but for the extra 'shimmer' and detail I gained in the bass with the AIV magnets, I found the top end now had a 'stiffer' and more 'toothy' sound. I changed back to AIIs - as for me that is the real Stormy Monday voice at it's best.
For your needs, I am thinking 'Mules' also ( or even something a touch hotter if really tight is your preference ) and do bear in mind that although the online shop does not ask which magnet you need in the Stormy Monday and assumes you want AII - you can contact Tim at B.K.P directly for 'special requests'- and of course excellent advice ! :)
The Mule is wound / voiced around an AIV magnet ( and very nice too - as I have a set in a Les Paul ). Unfortunately I cannot compare them to Burstbuckers, as my Lester came with 498/490 pickups. The Mules where profoundly better than those in the sweetness and clarity stakes . 8)
I did leave some sound clips of AII and AIV stormies in an Archtop in the Player's section last year, but I have not attached links to them at this stage , as they are in a fully hollow guitar, so the comparison between AII and AIV is apparent , but the suitability for your purpose is not really confirmed by them as such.