If you had the car running fine with VE, then tuned the MAF you were already out of speed density, do you mean you tuned the VE, then Did the Maf, all was good then you turned fuel trims on and it went haywire?
Speed density means the Maf is turned off, you cant tune the Maf if you are still in speed density, maybe you tried tuning the maf when you were really still not using it?