Best way to migrate clients to another IP block

I have a legacy network with a single vlan interface on a core network configured with a IP address and 4 secondary IP addresses. Someone just kept adding secondary IP addresses when there were too many users in one block... I can see 1500 different MAC addresses there currently.

You'll have to remind me how the IP helper works here :) If a client connects to a network where the router has 5 IP addresses, how does it send DHCP requests? Does it send a DHCP request with all the 5 different source addresses and give client the first one it gets back, which might be from any of those 5 IP blocks?

What would be the best way to migrate these to a single IP block, the fifth one with a /22 mask? Can I make the first 4 DHCP scopes smaller to force the DHCP server to lease IP addresses only from the last block? Or do I need to contact the persons managin this switch (management of the switch has been outsourced for some reason...) and ask them to change the /22 block as the first one? Are there still changes that a DHCP server would lease addresses from the other blocks?

Thanks!