Dear Vadim,
I only understand that your Vlan segment is very large.
Try to segmentise you Network in more nos of vlans.
E.g. as you say there are 2000 nos of Host in the same vlan you need to create 8 - 9 vlans.
All Vlans will be created on 3750 switch and inter-vlan routing will be done by 3750 switch only.
Give the default route to your router for outside communication.
Using this solution you can make your broadcast domain very small of arounf max 254 hosts.
This will make your nwtwork stable as as larger your broadcast domain (in your case is of around 2000 nos of hosts), your network have larger chances of network instability.
Than why don;t you go for the solution shown. You have all the resources which are required.
Hope I understand your problem and this will help you.
Do not forget to rate the post.
Regards,
