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I'm really not up on the LS1 performance parts. Don't know the HP/RPM break on LS1 headers. I'm pushing 800 HP/7,200 RPM redline through 1-3/4" mid-length headers. Dyno testing has not identified any issues with the exhaust system on the car. I did buy a set of 1-3/4" long tubes, based on dyno testing on a friends 1,000+ HP S/C LT1, but never got around to installing them. The problem with larger primary tubes is that due to low velocity they are not as effective at scavenging at low RPM. Scavenging helps pull more air/fuel mixture into the combustion chamber, and pull more burnt gasses out during valve overlap. Larger diameter primaries can also create problems at low RPM due to "reversion", where exhaust gas can flow backwards and mix into the incoming air/fuel charge. One solution is a "step" header, where the first couple inches of the primary that bolts to the head is slightly smaller than the rest of the primary. An example would be a 1-3/4" section at the head, followed by 1-7/8" from there to the collector.
For your usage, stock engine, focusing on street driving I would guess that the 1-3/4" would be OK. It would be good if we had some LS1 owners with more modification experience to help out here.
As to the Y-pipe issue, t don't know the details of the LS1 exhaust. Also need to know the emissions laws enforced where you live. If the local jurisdiction enforces Federal law, the cats cannon be relocated from the stock position. Several states utilize the California CARB-EO certification on headers, which follow Federal regulations, and require a tag welded to the headers showing the CARB-EO approval number. You have to determine that locally. Typically, a CARB-EO compliant header will couple to the stock Y-pipe. Non-compliant headers will typically offer a proprietary Y-pipe to allow the headers to connect to the stock (or aftermarket) intermediate pipe.