I remember your restoration project from the fall. Fine job and it sounds like your father is enjoying your work. You can't go wrong with the advice given above for tires. There is a 27" tire (630) thread in the stickies. I think the widest available is 35-630. BikeTiresDirect.com has a reasonable selection. How wide a tire you can use is going to be up to the rim, but if you have the concave Weinmann rims mentioned above, the OEM specs are in the attached figure.
I ride the local MUPs (crushed limestone, recycled asphalt) and the county maintained dirt roads with 28-630 or 32-630 tires. In the spring when the path is wet, the slightly more aggressive tread of the Continental Tour Ride (32-630) was more sure-footed. When the path is dry, 28s are fine. I've no experience with the 35mm tires though Spring is coming.
