How do Southern Baptists who believe in the immortality of the soul explain what death means in scripture

As in much of Protestantism, there is much protesting and not much consensus. Because of their strong belief in congregational autonomy (mentioned in the SBC's positional statements while the resurrection is ignored), many Southern Baptists are left to decide for themselves what they think the resurrection will entail as it's not seen as critical a point as things like congregational autonomy, soul competency, and baptism by immersion.

The June 2014 issue of SBC Life affirms my evaluation:

Amillennialists and premillennialists of every variety coexist in all realms of Baptist life, with proponents of each position affirming the inerrancy of Scripture and hardly anyone regarding differing positions on the millennium as an obstacle to cooperation in missions, theological education, evangelism, or cultural engagement.

In my experience in the Southern Baptist church, the prevailing opinion is that the death which (nearly) everyone experiences involves the transition from a sinful, earth-bound being to a sinless, 'spiritual' being in the presence of God.

As mentioned previously, there is no consensus opinion on the second coming (including the resurrection) because it isn't central to Baptistism. Many Southern Baptists interpret St. John's Revelation to mean Christ will destroy all His creation in favor of sustaining them (Southern Baptists) as incorporeal beings. This belief enjoyed enough popularity to cause NT Wright to write a book against it.

According to my Southern Baptist, undergraduate education, they also have an opinion of the second death. It is not, they say, related to any manner of transition but rather a termination of all comfort and pleasantries as they are sustained by God to the ages while being tortured for rejecting Him. They believe the damned are eternally consigned to rebellion against God with no hope of escaping His unimaginable torture.

Unfortunately, I believe any answer on this front is of limited use as I am certain there are Southern Baptists who disagree. This is a reflection of my personal experience and opinion that Southern Baptists are less likely to be concerned with the resurrection than with doctrinal issues such as the perseverance of the Saints, Christian exclusivism, Biblical inerrancy, and predestination.

Well, my education is Free Will Baptist rather than Southern Baptist, but I can give you a straight answer to your question that my Southern Baptist preacher brother in law would sign off on. It is quite simple. When you read, "the wages of sin is death", that death is not referring to your heart stopping, it is indicates eternal damnation and separation from God. What we call death in today's terms is referred to as "sleep" in the scriptures. If we die (our heart stops beating) and we have entrusted our heart to Christ, we will never experience the death referred to in the scriptures but only eternal life.

The Southern Baptist position is that we will be resurrected with physical bodies, as they state in The Baptist Faith and Message:

X. Last Things

God, in His own time and in His own way, will bring the world to its appropriate end. According to His promise, Jesus Christ will return personally and visibly in glory to the earth; the dead will be raised; and Christ will judge all men in righteousness. The unrighteous will be consigned to Hell, the place of everlasting punishment. The righteous in their resurrected and glorified bodies will receive their reward and will dwell forever in Heaven with the Lord.

I would not phrase the destination of our resurrection "Heaven", because it does suggest a mode of living far different from what we know now, but they do at least give Revelation 20-21 in the references supporting this position, which teaches the "new heaven and a new earth". Perhaps the lack of clarity here represents a lack of consensus as to whether the new earth should be understood as a renewal, a transformation, a purging, a destruction and recreation, or somewhere else on that spectrum. (To be fair, I doubt that there are many other denominations of comparable size that also wouldn't have a lot of disagreement over the origin of the new earth.) But in any case, it is clear that, whatever a "glorified" body is, our destiny is not to change from a physical to a spiritual being, as the question suggests.