The Greyhound is close to a T-70 in terms of AI power. Its 4 CP timing is fine in 1v1. It needs that gate otherwise it would become too powerful. It was heavy meta before Mechanized took over. It's too bad that 4 CPs is too late for teamgames, but you can't buff its timing without potentially breaking it in 1v1. So there's not much to be done. Some units are simply only good in one mode.
Couldn't you theoretically tinker with Main Gun/50 Cal DPS and gate some of it's AI potential behind tech? For example slightly improve the main gun so that vanilla Greyhound is viable at a slightly earlier timing and gate the 50 Cal behind Major tech so that Greyhound isn't too oppressive early on. IMO it would go a long way to helping the commander so that Greyhound isn't so dependent on munitions to be good when the rest of the commander abilities also require munitions- making it rather difficult to fully utilize this commander.
Edit #1 I suppose you could also make the 50 Cal a Vet 2/3 requirement where it's only available/Free? after you hit that Vet.
Edit #2 Another idea would be to increase main gun damage at Vet 1 so that you can't abuse Greyhound as emergency AT but it scales better in that department.