wore out is right, John Deere type 303 Special Purpose Oil, went away when the Endangered Species Act was passed about 1974 as Sperm whale oil was an ingredient in 303, and could no longer be obtained. Oils advertised as 303 currently are basically junk and there have been lawsuits and bans on the sale of such in a number of places. Hy Gard is the replacement and is backwards compatible for use where 303 was called for. The current JD spec to look for in a UTHF claiming to be for use in John Deere Equipment is J20C.
If the Harvest King UTHF says it meets the J20C spec on its label or product data sheet it should be satisfactory to use. I think their Premium grade meets that spec, but suggest one confirms that on the product they purchased, for themselves.
I think 10W falls in the 20 to 30 ISO range. Regular Hy Gard is in the ISO range between 46 and 68 (Low Viscosity Hy Gard is in the ISO 32 range). The recommended Hy Gard is thicker than the 10W you asked about.
As noted, leaks are much more likely caused by worn/damaged seals, gaskets, and hoses than thin oil.
If he doesn't have the Operator's Manual, he/you can download and save a free pdf copy from the JD Ag & Turf Bookstore. Use the Equipment Publication button to do a model search for 830.
JD Ag & Turf Bookstore