Johnathan,
That solution would not work, because both physical links of the same LAG/Etherchannel should terminate on the same switch. You can't "split" it between the two different switches.
The best solution would be to use 2 LAGs, one for each Cisco stack. You could then use RSTP to minimise the downtime in case of link failure or if your Cisco switches support it, you could use REP protocol instead.