Small Engine Warehouse states deep within the fine print on its website: "About half of the engines we purchase are surplus stock..."
Buying an engine from them is far more risky than buying through an authorized Honda retailer, and it isn't a risk everyone should take.
There is a pretty good chance the engine you bought from them had some sort of "event" occur between when it left the Honda factory and when you received it, and there is no way you will ever know.
All you know is that you have an engine that doesn't run right, bought from someone who doesn't seem terribly concerned about doing whatever it takes to satisfy their customer.
If this were my problem I wouldn't hold my breath waiting for Small Engine Warehouse to fix it.
It will likely cost you a lot more in time and frustration to prevail upon them to try to resolve this than to just fix it yourself - and by fixing it yourself you will probably learn a bit about your engine too.
First, make sure the carburetor is a correct model for a GX35 engine (and preferably for YOUR model of GX35). As long at the carb is "a" carb for a GX35 though, it will probably work reasonably well.
Second, it seems that you have already found that the O ring is too large. A new one is cheap, so just replace it.
If after you have verified that the carb is correct and the intake O ring is a proper fit - and it still doesn't run right - then I would get a bit insistent with Small Engine Warehouse to do whatever it takes to resolve this matter.
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Chad,
I made the above post before reading your latest posts.
The Honda GX35 uses a Walbro WYB - but there are MANY different models of WYB carbs for many different engine applications. They may all look alike and bolt right on to your GX35, but will not necessarily work correctly. Just because someone offers a WYB carb and says it is for a Honda GX35 does not make it so. You need to verify application by part number. As a practical matter though, if a Walbro WYB is for some model of GX35, it will likely work "OK".
First things first though, I would deal with the O ring. That may likely be your only problem. If it doesn't run right with a good O ring, THEN I would start checking carb part numbers.