I'd suggest confirming that the 10,000-pound rated receiver hitch has enough tongue weight rating to handle your trailer. This subject has come up various times with similar 8,000-pound receivers that only had 500-pound tongue weight ratings; thereby effectively limiting towing capacity below the 8,000 pounds.
I don't know if the same applies to the 10,000-pound receiver you're considering, but I'd check into it just to make sure.
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