1. There is no way to snake a new HDMI by pulling with the old bad cable. You also have the problem with the large HDMI connector getting thru the RV.
2. A way to do the fix is to purchase a HDMI IR extender
https://www.amazon.com/HDMI-Extender-Over-CAT5-CAT6/dp/B07WMVMHDV/ref=sr_1_20?dchild=1&keywords=hdmi+extender&qid=1604928043&sr=8-203. Using the IR extender, you will NOT have the cost of a 30 foot HDMI cable which is probably more than the extender cost. Doug
PS. HDMI cables DON'T go bad. There are 2 things that make a defective HDMI cable
1. A Screw or the cable is pinched
2. MOST COMMON. People constantly disconnect the HDMI from the appliance or TV and pull by the cable instead of the connector housing. HDMI cables are very fragile at the end connectors.