Aecro,
Q : Is it possible to connect each Cisco access switch to each of the two backbone switches, without having spanning-tree shutting one link down?
A : No
Distributed Trunking is a feature of the "full" ProVision chipset switches such as the 3500yl/5400zl/6600/8200zl. It is not available on the 2810
Incidentally, the 2810 switches do not "stack" in the way that most engineers would define stacking. They only offer "legacy" HP stacking which is little more than an IP conservation offering. If you want a proper stack within the "ProCurve" portfolio where you can terminate a LAG (Cisco etherchannel) on different switches, then either the 3800 (layer 3) or 2920 (layer 3-ish) switch are your best options.
Regards,
Peter