hi Adrian
I make advice to you two distribution switch on your system for redandacy and full time working and each 2824 switch two connect to each core distribution switch.
in this way each 2824 switch to connect network core with 2Gbps uplink port.
on 2824 switch one uplink port down is working other uplink port with 1Gbps connection.
this methot name Hp trunking
and you make STP config (with trunk config)
STP loop free topology protocol
you connect two core switch between hight bandwith connection ten gigabit or 4 gigabit trunk and each 2824 switch sperate two uplink port frist uplink port connect frist core switch ,secont uplink port second core switch
example config :
1core5400(config)#trunk 15-18 trk1 trunk
1core3500(config)#trunk 10 trk2 trunk
1core5400(config)#spanning-tree
2core5400(config)#trunk 15-18 trk1 trunk
2core3500(config)#trunk 10 trk2 trunk
2core5400(config)#spanning-tree
2824(config)#trunk 23-24 trk2 trunk
2824(config)#spanning-tree
cenk