for bells and most other instruments, he says they produce totally different overtones and are thus not suitable for playing chords
This is true in general. However, it is possible to tune the inharmonic overtones of an idiophone by shaping the instrument, which can enable them to play chords. The marimba and vibraphone are notable examples. From Wikipedia's vibraphone article:
These rectangular bars have three primary modes of vibration. The deep arch causes these modes to align and create a consonant arrangement of intervals: a fundamental pitch, a pitch two octaves above that, and a third pitch an octave and a major third above the second. For the F3 bar that usually forms the lowest note on a vibraphone, there would be F3 as the fundamental, F5 as the first overtone, and A6 as the second overtone. ...
After beveling or rounding the edges, fine-tuning adjustments are made. If a bar is flat, its overall pitch structure can be raised by removing material from the ends of the bar. Once this slightly sharp bar is created, the secondary and tertiary tones can be lowered by removing material from specific locations of the bar.
which synthesized sounds are suitable for chordal playing and which are not[?]
The best way to determine this is to use your ear. But you can use the information above to help you understand what's going on. Synthesis of bells and other idiophones is achieved by using inharmonic overtones, and just as with natural sounds, the degree to which these overtones approximate the harmonic series determines their usefulness in chords.
Handbells have been mentioned in the comments. These are also manufactured with attention to the relationship between the fundamental pitch and the overtones. From Wikipedia:
The overtones on an English handbell are a 12th (an octave and a perfect fifth) above the fundamental, while Dutch handbells – such as Petit & Fritsen – focus on the overtone a minor 10th (an octave and a minor third) or a major 10th (an octave and a major third) above the fundamental.
In fact, inharmonicity is also a feature of strings unless the oscillation is driven (with a bow).
This leads to stretched tuning in pianos and various problems with guitar intonation.