you can setup multiple “bonding” interfaces in 802.3ad mode (LACP) in a single bridge. Always make sure you take the internal topology of the router into account - for a 4011, one interface in each 2-link bond should be chosen from ether1-ether5 and the other one from ether6-ether10:
You can use multiple VLANs on the same bridge, too.
VRRP and bridge are not mutually exclusive. You can have two routers, both connected using two LAGs to a pair of switches, and use VRRP in some or all VLANs.
If you cannot/do not want to make a stack of the two core switches, the interconnection between them should also be a LAG. I also don’t get why the access switches are always connected only to one core switch.