Let's get a few things straight before moving on. Adding sparge slowly or draining it out slowly are requirements of fly sparging and time wasters in batch sparging. If anyone empirically finds that slowing anything down during a batch sparge increases efficiency, it's because you're allowing for more starch conversion (meaning you weren't fully converted after your sacc rest). This can be attributed to being way off on your initial mash temps due to bad thermometers, a really coarse crush, or pH being way out of whack (less likely). One of the first troubleshooting steps is to test the gravity of the first wort (take a sample during vorlauf) and compare that against the theoretical gravity (100% conversion) of your mash. This will rule out a conversion issue vs. a lauter/sparge issue.
it hasn't been brought up, but how about a picture of the inside of your mash tun? How much dead space do you have?