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You mentioned that your "TV" has a tongue weight limitation of 600lbs...., but I would also confirm the weight ratings of your OEM Class III receiver (some are rated 500/5,000lbs, others 600/6,000lbs). Also confirm the "Weight Carrying" and "Weight Distribution" limitations on your OEM receiver. If there isn't a "Weight Distribution" rating stamped on the OEM receiver then a WDH can't be used. Good to know if you have any other restrictions before looking into a WDH.
Check the A-frame of the 19H for a WDH limitations/restrictions, some of the smaller HTT's have them.
If you will be towing with a loaded tongue weight of 500lbs-600lbs (max), IMO a properly sized WDH (if allowable) would enhance the towing experience.