Radiant heating consists of a grid of copper pipes in your concrete floor that carry heated water. The pipes heat the concrete floor, and that "radiates" heat evenly throughout your home . When those water-filled pipes deteriorate, the resultant leaks can do substantial damage to your home. An inspection hole cut into the concrete floor where the water surfaces is the only way to do a permanent repair. The excavation also will reveal the general condition of the system.
Our guess is that your 30-year-old system may well be on its last leg. Since Eichler homes have neither crawl nor attic spaces, alterations to electric, plumbing and heating are a challenge. Central heating could be ducted "over the roof", but that would be unsightly and expensive, and it would make future roof repairs extremely difficult to perform. Electric baseboard heating, even the kind that heats water, is less expensive to install but costs more to operate. And, inhibits decorating.
We normally would not recommend a gas-fired wall furnace. They are not revered for providing balanced heating. But they are cost efficient to operate, and, considering the restrictions posed by the structure, a viable alternative. A gas line could be run from your garage, over the roof and down through a wall. Two furnaces, one in the bedroom hall and one in the living room or family room would do the trick. Separate thermostats could be used to turn the bedroom wing off while the rest of the house was being heated.