According to the project the 8 ohm side has two connectors, and the 1200 ohm side has three. I hooked it to the 8 ohm side.
The one shown in the project has a single 8 ohm winding and a center tapped 1000 ohm winding. The center tap lead is left unused. If your transformer has an 8 ohm winding and a 1200 ohm center tapped winding, you still need to identify and use the correct leads to connect to the same locations in the circuit.
I tried two different radios, one with a digital tuner I was able to set up to 1000 kHz exactly.
With this information, I'll assume that you are using a 1 MHz oscillator, otherwise, your radio and oscillator are at different frequencies so it isn't going to work. A digital AM tuner isn't very helpful in diagnosing a problem as it will only tune to the exact carrier frequency so you can't determine if you are producing that carrier frequency by slowly tuning through that frequency. Assuming your 1000 KHz oscillator is working, with an analog tuner tuned to 997 kHz, you would get a 3 kHz squeal (difference between the carrier and the local oscillator in the radio). This squeal would reduce to 100 Hz as you slowly tune to 999.9 kHz and then disappear and then reappear as it is tuned to 1000.1 kHz and increase in pitch to 3 kHz as it is tuned to 1003 kHz.
I am in Halifax, NS, and there appear to be no radio stations past 920.
That is surprising. A quick check of stations in Nova Scotia between 900 and 1350 kHz shows: CJCH 920 Halifax, CHER 950 Sydney, CHNS 960 Halifax, CKBW 1000 Bridgewater, CBI 1140 Sydney, CKEC 1320 New Glasgow, CJLS 1340 Yarmouth, CKAD 1350 Middleton.
If your radio isn't picking up a 10 KW CHNS 960 in Halifax during the day, your AM receiver has some problems. At night, CHNS is directional and if you are south west of its towers, then it is understandable that you won't pick it up.
The 1.2288 MHz oscillator might be a better choice for your area. CKBW 1000 Bridgewater is a 10 KW station about 60 miles away. During the night, it uses a directional pattern to send its signal toward the east toward Halifax.
Note: 1.2288 MHz can't be properly tuned by a commercial digital tuner as they only tune to every 10 kHz.