A few years ago I received an email from a former student (now a young pastor) asking some questions about speaking in tongues during corporate worship. Let me excerpt his e-mail and then include my reply (with his permission):

Dr. Berding, I am emailing you because I have a question about ‘service of worship’ for the church. Recently I have taken upon myself to work out some position papers on where I stand on a few ecclesiology topics. I have spent time reading from Horton, Grudem, Bloesch, and some of Clowney's works on ecclesiology. However, recently at our corporate worship one of the elders prayed in tongues and this was followed by what appeared to be an interpretation. As I have been reading through these books and wrestling with scripture, I have come to wonder if tongues plays a role in corporate worship or not. The sources I have only address whether tongues are for today or not, but not whether or how they should be used in corporate worship. I realize that this is a discussion that is debated among many denominations and that there are a vast number of books on the topic. This is my first time really wrestling with it, so I was wondering if you had any pastoral insight in dealing with this or if you could point me in a direction of some books for more study.
Dear Jeff,
Wonderful to hear from you … and it was really good running into you in the hallway outside my office a few weeks ago!
On tongues, my recommendation is that you stay close to the Bible. I'm unimpressed by the exegetical arguments for cessationism (but won’t review them today). This means that I'm left with what the Bible teaches on the topic.
The go-to text, of course, is 1 Corinthians 14. There you will discover the following ideas:
  1. Paul doesn't allow us to completely forbid speaking in tongues (v. 39, 26).
  2. There is a place for personal use of tongues outside of the community (vv. 4, 17-19, 28).
  3. Everything should be done properly and in order (v. 40, 33).
  4. The goal is edification of the church (vv. 5, 26).
  5. Only one person at a time should speak in tongues, and no more than two or three in a meeting (v. 27).
  6. Each should speak in turn (v. 27, 31).
  7. Wait for an interpretation (v. 27).
  8. If no interpreter, either: a) the tongues-speaker should ask for an interpretation, or b) the tongues-speaker should keep silent (vv. 13, 28).
  9. Emphasize prophecy over tongues (throughout)
  10. Test everything (vv. 29, 37-38)
One thing to keep in mind, though, is that Paul wrote these words in the context of house churches (50 people max; 10-25 more likely). This means that if someone stands up during a large worship gathering and claims that he should be permitted to speak in tongues based upon 1 Cor. 14:39, I would consider that to be an inappropriate application of that text (because of the different setting). But to completely disallow speaking in tongues anywhere in the life of the church also seems problematic.
One more thing. Keep in mind that false tongues exist (as the tongues found in Buddhism, Hinduism, and Sufi Islam all demonstrate), so you’ll need to be discerning.
Sorry, I don't have a good go-to source on this. I would probably be closer to Grudem on the particular issue of tongues than the other authors you mentioned in your e-mail.