You're definitely not alone with a loose shift lever in the BA10! A common issue with these gearboxes is worn bushings or a loose linkage. Here's a few things to consider:
Linkage adjustment: Sometimes, the shift linkage can get out of whack. Double-check the adjustments and tighten any loose bolts.
Bushings: Inspect the shift lever bushings—these can wear out over time and lead to sloppiness. Replacement bushings are usually pretty affordable and can make a significant difference.
Shifter plate: If your shifter plate is worn, it can also contribute to a loose feel. You can try reinforcing it or replacing it.
Oil level: Make sure your transmission is at the correct oil level. Low fluid can lead to poor shifting performance.
By addressing these issues, you might be able to tighten things up without needing to invest in a new transmission. Good luck with it, and keep us posted on your progress!