SOI has some relevancy, other indicators have gotten perhaps washed out from implementation/usage over time, but I've seen where other things were acting peculiar and the SOI took its leading role. Something I also watch is the NOI and SOI* (southern hemisphere NOI), these extend pressure measurements to 30N/30S, connected with the same pressure origin region as SOI. I haven't found anything that has a clear definitive +weeks/months lead but the subsurface. In other words, if the SOI is not strongly negative now, that has already been factored into current SSTs, although perhaps you could sort out a correlation there.
(We had a major +NOI in February, just like the last 6 February's.. so trends may be somewhat the same through May/June. We would need a super -NOI to break that trend. )