Mike, here's a picture of the hose I used, was wire reinforced, perhaps could have done with regular, but what the heck, it's a boat! The hose, all 14 feet of it, cost $46.20 plus tax. I'd recommend wire reinforced anyway, since the damage to the old hose is plain to see, so regular hose would "die" more quickly, out of sight, out of mind.
I need to check again on the connection sizes at the heater because the 5/8 size could very well go all the way to the heater, and the barbs and extensions there seemed only to be for ease of connection of the then-new heater by the PO. In reviewing my pictures, it appears they could be the same size hose. At least those hoses, from the heater end of my new hoses to the heater, are not 20 years old, only 9 or 10. Thanks for noting that fact. Now I can kick myself for not going all the way!

Folks, get at least EIGHT feet of new hose. Mike's point is well taken, the new hose length depends on where your connections on the heater are located.
Tag line: In retrospect, I could have done it without the tag line, because as you and Craig mentioned, it is a push as well as pull effort. But I only knew that after I got the first hose through and found that I could reach it from the door. The tag lines helped immeasurably, though, because of that tight bend where the two hoses both go through the two holes in the engine space. There's that first little spot where one is actually on top of the other one, and then they seem to slide off to be next to each other. I pulled the first (forward) hose through only to the tag line, then started pushing the aft hose through the hole and needed to use an angled screwdriver to get the second hose to "bend" enough to turn 90 degrees. It would be doable without the tag lines, but I'm glad that I used the lines. Part of that approach came from running new wiring to our new alternator last year, so I got into the "tag line mode." Since I had to trim the heater ends of the hoses, the holes I put into the hoses got cut off anyway.
Thanks again for your help.