Which would you consider to be the proper way to incorporate crossfit into a regular strength training program ?
It seems as though the two types of work outs are contradictory in a sense that one is designed for extreme cardio conditioning, and the other for pure strength. That being said, which is the proper balance of cross fit and strength training. This question is more inclined to the experienced weight lifters and strength coaches.
You can incorporate any exercise you see fit and proper in your workout routine.
I'm not sure if there is a "proper" balance between the two, but the first question I would ask you is what is your ultimate goal?
Seems like CrossFit incorporates many facets of fitness--including strength--but also power, endurance, agility, etc... It would also depend on how many days a week you are currently weight training.
I would not label the workout Crossfit, I would consider it either H.I.T or conditioning. As you said, there's a fine line with conditioning and high volume resistance training and at some point fatigue sets in and form breaks.
I would recommend either separating the two workouts, one day of conditioning type exercises and one day of resistance training. You can also do both together by having a workout that includes aspects of both. A sample workout can be: cleans, DB chest press, renegade rows, split squat, and prowler push/pull done circuit style or timed intervals.
Hope this helps.
Thanks for your replies!