If You want just to distinguish ALIX and APU boards, You can just parse first three octects of MAC address of Your PC Engines board. These three octets are unique for each Network Controller chip vendor.
IIRC ALix board have VIA NICs, apu1 has Realtek NICs, and apu2 series boards have Intel NICs. They should have different first 3 octets in MAC address.
Also If You have access to Your dhcp server configuration You can define each board to obtain specific IP address depending on MAC of the board. GIven that You can define IP groups gathering ALIXes and APUs separately.
If I am not mistaken You can pass different filename and next-server dhcp options to each group.