Don't call the unweighted item sums "factor scores". Even if the items were continuous and you were using a weighted sum, the scores would not be the same as, or even necessarily good estimates of, the theoretical factors in a factor analysis. Call them "scale scores" (or something similar). Such scales are the norm, rather than the exception, and treating them as equal-interval measures in further analyses is standard practice, even with as few as 7 items. The scales are far more than purely ordinal; the "true" differences between scale scores are unlikely to be so unequal that treating them as equal will be substantively misleading. The real problem is not so much the inequality of the true intervals as it is the loss of information about differences between people with the same score that comes as a result of having only a few different score values.
Whatever you do, don't use Spearman correlations (or anything else that converts the data to ranks and then uses the ranks as if they were on an interval scale), because that confounds the intervals between scale scores with the proportion of people having each score. Spearman correlations should be used only when there are few ties in the data, when the number of different scores is almost as big as the number of people.