Sounds like they don't want one L2 switch to connect to another L2 but L3 to L3 is fine, along with L3 to L2.
Your 3750G switches are L3 switches, so even at the edge you can run them just as L2 or use them as L3. (Stacking them, via 3750 stack cables, I suspect, probably has nothing to do with cascade restrictions.)
If you connect your 3750G uplink to another L3 device, and don't connected multiple 3750G edge devices directly to each other except via the special stack cable (if more than one), then you should be fine as long as you also configure IGMP snooping for your edge VLANs.
You didn't ask about multicast routing, so I assume you understand that.
We are pleased to announce availability of Beta software for 16.6.3.
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