I'm no expert on these old heaters, but I'd think if both hoses are heating up water must be flowing through the core. I'd never heard of bleeding the core until I started playing with later stuff.
I don't think my problem is heat as much as it is moisture and that problem will remain until I get deep into the restoration of the body, something that is still a few years off.
In just a few minutes looking I found a 'street rod heater' that looks like it could be fit under or behind the seat of many trucks, and this is a brand new one so no worries about the core.
Mojave Universal Heater. Measures only 10-1/4" wide, 9" deep and 5" tall. Less than $200 so not pocket change, but not second mortgage kind of money either.